KILLED proof of input_N4woEzCTcc.trs # AProVE Commit ID: aff8ecad908e01718a4c36e68d2e55d5e0f16e15 fuhs 20220216 unpublished The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF).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), 141 ms] (12) CpxTypedWeightedCompleteTrs (13) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (14) CpxRNTS (15) SimplificationProof [BOTH BOUNDS(ID, ID), 0 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), 4 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), 4 ms] (38) CdtProblem (39) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1 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), 0 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), 5 ms] (56) CdtProblem (57) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (58) CdtProblem (59) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 22 ms] (60) CdtProblem (61) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (62) CdtProblem (63) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (64) CdtProblem (65) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 17 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), 0 ms] (72) CdtProblem (73) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (74) CdtProblem (75) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (76) CdtProblem (77) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (78) CdtProblem (79) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (80) CdtProblem (81) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (82) CdtProblem (83) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (84) CdtProblem (85) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 9 ms] (86) CdtProblem (87) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 27 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), 3 ms] (94) CdtProblem (95) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (96) CdtProblem (97) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 22 ms] (98) CdtProblem (99) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (100) CdtProblem (101) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 36 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), 10 ms] (108) CdtProblem (109) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 30 ms] (110) CdtProblem (111) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 5 ms] (112) CdtProblem (113) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 110 ms] (114) CdtProblem (115) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (116) CdtProblem (117) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 24 ms] (118) CdtProblem (119) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (120) CdtProblem (121) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 24 ms] (122) CdtProblem (123) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 2 ms] (124) CdtProblem (125) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 139 ms] (126) CdtProblem (127) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (128) CdtProblem (129) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 95 ms] (130) CdtProblem (131) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 34 ms] (132) CdtProblem (133) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 200 ms] (134) CdtProblem (135) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 13 ms] (136) CdtProblem (137) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 91 ms] (138) CdtProblem (139) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 26 ms] (140) CdtProblem (141) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 78 ms] (142) CdtProblem (143) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 17 ms] (144) CdtProblem (145) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 99 ms] (146) CdtProblem (147) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (148) CdtProblem (149) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 99 ms] (150) CdtProblem (151) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 59 ms] (152) CdtProblem (153) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 116 ms] (154) CdtProblem (155) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 23 ms] (156) CdtProblem (157) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 243 ms] (158) CdtProblem (159) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (160) CdtProblem (161) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 119 ms] (162) CdtProblem (163) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 12 ms] (164) CdtProblem (165) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 334 ms] (166) CdtProblem (167) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 52 ms] (168) CdtProblem (169) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 185 ms] (170) CdtProblem (171) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 54 ms] (172) CdtProblem (173) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 135 ms] (174) CdtProblem (175) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 41 ms] (176) CdtProblem (177) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 172 ms] (178) CdtProblem (179) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 61 ms] (180) CdtProblem (181) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 122 ms] (182) CdtProblem (183) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 26 ms] (184) CdtProblem (185) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 95 ms] (186) CdtProblem (187) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 51 ms] (188) CdtProblem (189) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 132 ms] (190) CdtProblem (191) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 27 ms] (192) CdtProblem (193) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 108 ms] (194) CdtProblem (195) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 38 ms] (196) CdtProblem (197) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 138 ms] (198) CdtProblem (199) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 62 ms] (200) CdtProblem (201) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 253 ms] (202) CdtProblem (203) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 88 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)) mark(terms(X)) -> a__terms(mark(X)) mark(sqr(X)) -> a__sqr(mark(X)) mark(add(X1, X2)) -> a__add(mark(X1), mark(X2)) mark(dbl(X)) -> a__dbl(mark(X)) mark(first(X1, X2)) -> a__first(mark(X1), mark(X2)) mark(cons(X1, X2)) -> cons(mark(X1), X2) mark(recip(X)) -> recip(mark(X)) mark(s(X)) -> s(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) 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)) mark(terms(X)) -> a__terms(mark(X)) mark(sqr(X)) -> a__sqr(mark(X)) mark(add(X1, X2)) -> a__add(mark(X1), mark(X2)) mark(dbl(X)) -> a__dbl(mark(X)) mark(first(X1, X2)) -> a__first(mark(X1), mark(X2)) mark(cons(X1, X2)) -> cons(mark(X1), X2) mark(recip(X)) -> recip(mark(X)) mark(s(X)) -> s(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) 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)) mark(terms(X)) -> a__terms(mark(X)) mark(sqr(X)) -> a__sqr(mark(X)) mark(add(X1, X2)) -> a__add(mark(X1), mark(X2)) mark(dbl(X)) -> a__dbl(mark(X)) mark(first(X1, X2)) -> a__first(mark(X1), mark(X2)) mark(cons(X1, X2)) -> cons(mark(X1), X2) mark(recip(X)) -> recip(mark(X)) mark(s(X)) -> s(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) 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] mark(terms(X)) -> a__terms(mark(X)) [1] mark(sqr(X)) -> a__sqr(mark(X)) [1] mark(add(X1, X2)) -> a__add(mark(X1), mark(X2)) [1] mark(dbl(X)) -> a__dbl(mark(X)) [1] mark(first(X1, X2)) -> a__first(mark(X1), mark(X2)) [1] mark(cons(X1, X2)) -> cons(mark(X1), X2) [1] mark(recip(X)) -> recip(mark(X)) [1] mark(s(X)) -> s(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] 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] mark(terms(X)) -> a__terms(mark(X)) [1] mark(sqr(X)) -> a__sqr(mark(X)) [1] mark(add(X1, X2)) -> a__add(mark(X1), mark(X2)) [1] mark(dbl(X)) -> a__dbl(mark(X)) [1] mark(first(X1, X2)) -> a__first(mark(X1), mark(X2)) [1] mark(cons(X1, X2)) -> cons(mark(X1), X2) [1] mark(recip(X)) -> recip(mark(X)) [1] mark(s(X)) -> s(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] The TRS has the following type information: a__terms :: recip:s:terms:cons:0:nil:first:sqr:add:dbl -> recip:s:terms:cons:0:nil:first:sqr:add:dbl cons :: recip:s:terms:cons:0:nil:first:sqr:add:dbl -> recip:s:terms:cons:0:nil:first:sqr:add:dbl -> recip:s:terms:cons:0:nil:first:sqr:add:dbl recip :: recip:s:terms:cons:0:nil:first:sqr:add:dbl -> recip:s:terms:cons:0:nil:first:sqr:add:dbl a__sqr :: recip:s:terms:cons:0:nil:first:sqr:add:dbl -> recip:s:terms:cons:0:nil:first:sqr:add:dbl mark :: recip:s:terms:cons:0:nil:first:sqr:add:dbl -> recip:s:terms:cons:0:nil:first:sqr:add:dbl terms :: recip:s:terms:cons:0:nil:first:sqr:add:dbl -> recip:s:terms:cons:0:nil:first:sqr:add:dbl s :: recip:s:terms:cons:0:nil:first:sqr:add:dbl -> recip:s:terms:cons:0:nil:first:sqr:add:dbl 0 :: recip:s:terms:cons:0:nil:first:sqr:add:dbl a__add :: recip:s:terms:cons:0:nil:first:sqr:add:dbl -> recip:s:terms:cons:0:nil:first:sqr:add:dbl -> recip:s:terms:cons:0:nil:first:sqr:add:dbl a__dbl :: recip:s:terms:cons:0:nil:first:sqr:add:dbl -> recip:s:terms:cons:0:nil:first:sqr:add:dbl a__first :: recip:s:terms:cons:0:nil:first:sqr:add:dbl -> recip:s:terms:cons:0:nil:first:sqr:add:dbl -> recip:s:terms:cons:0:nil:first:sqr:add:dbl nil :: recip:s:terms:cons:0:nil:first:sqr:add:dbl first :: recip:s:terms:cons:0:nil:first:sqr:add:dbl -> recip:s:terms:cons:0:nil:first:sqr:add:dbl -> recip:s:terms:cons:0:nil:first:sqr:add:dbl sqr :: recip:s:terms:cons:0:nil:first:sqr:add:dbl -> recip:s:terms:cons:0:nil:first:sqr:add:dbl add :: recip:s:terms:cons:0:nil:first:sqr:add:dbl -> recip:s:terms:cons:0:nil:first:sqr:add:dbl -> recip:s:terms:cons:0:nil:first:sqr:add:dbl dbl :: recip:s:terms:cons:0:nil:first:sqr:add:dbl -> recip:s:terms:cons:0:nil:first:sqr:add:dbl 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__add_2 a__terms_1 a__first_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] mark(terms(X)) -> a__terms(mark(X)) [1] mark(sqr(X)) -> a__sqr(mark(X)) [1] mark(add(X1, X2)) -> a__add(mark(X1), mark(X2)) [1] mark(dbl(X)) -> a__dbl(mark(X)) [1] mark(first(X1, X2)) -> a__first(mark(X1), mark(X2)) [1] mark(cons(X1, X2)) -> cons(mark(X1), X2) [1] mark(recip(X)) -> recip(mark(X)) [1] mark(s(X)) -> s(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] The TRS has the following type information: a__terms :: recip:s:terms:cons:0:nil:first:sqr:add:dbl -> recip:s:terms:cons:0:nil:first:sqr:add:dbl cons :: recip:s:terms:cons:0:nil:first:sqr:add:dbl -> recip:s:terms:cons:0:nil:first:sqr:add:dbl -> recip:s:terms:cons:0:nil:first:sqr:add:dbl recip :: recip:s:terms:cons:0:nil:first:sqr:add:dbl -> recip:s:terms:cons:0:nil:first:sqr:add:dbl a__sqr :: recip:s:terms:cons:0:nil:first:sqr:add:dbl -> recip:s:terms:cons:0:nil:first:sqr:add:dbl mark :: recip:s:terms:cons:0:nil:first:sqr:add:dbl -> recip:s:terms:cons:0:nil:first:sqr:add:dbl terms :: recip:s:terms:cons:0:nil:first:sqr:add:dbl -> recip:s:terms:cons:0:nil:first:sqr:add:dbl s :: recip:s:terms:cons:0:nil:first:sqr:add:dbl -> recip:s:terms:cons:0:nil:first:sqr:add:dbl 0 :: recip:s:terms:cons:0:nil:first:sqr:add:dbl a__add :: recip:s:terms:cons:0:nil:first:sqr:add:dbl -> recip:s:terms:cons:0:nil:first:sqr:add:dbl -> recip:s:terms:cons:0:nil:first:sqr:add:dbl a__dbl :: recip:s:terms:cons:0:nil:first:sqr:add:dbl -> recip:s:terms:cons:0:nil:first:sqr:add:dbl a__first :: recip:s:terms:cons:0:nil:first:sqr:add:dbl -> recip:s:terms:cons:0:nil:first:sqr:add:dbl -> recip:s:terms:cons:0:nil:first:sqr:add:dbl nil :: recip:s:terms:cons:0:nil:first:sqr:add:dbl first :: recip:s:terms:cons:0:nil:first:sqr:add:dbl -> recip:s:terms:cons:0:nil:first:sqr:add:dbl -> recip:s:terms:cons:0:nil:first:sqr:add:dbl sqr :: recip:s:terms:cons:0:nil:first:sqr:add:dbl -> recip:s:terms:cons:0:nil:first:sqr:add:dbl add :: recip:s:terms:cons:0:nil:first:sqr:add:dbl -> recip:s:terms:cons:0:nil:first:sqr:add:dbl -> recip:s:terms:cons:0:nil:first:sqr:add:dbl dbl :: recip:s:terms:cons:0:nil:first:sqr:add:dbl -> recip:s:terms:cons:0:nil:first:sqr:add:dbl 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(cons(X11, X21)) -> cons(recip(a__sqr(cons(mark(X11), X21))), terms(s(cons(X11, X21)))) [2] a__terms(recip(X4)) -> cons(recip(a__sqr(recip(mark(X4)))), terms(s(recip(X4)))) [2] a__terms(s(X5)) -> cons(recip(a__sqr(s(mark(X5)))), terms(s(s(X5)))) [2] a__terms(0) -> cons(recip(a__sqr(0)), terms(s(0))) [2] a__terms(nil) -> cons(recip(a__sqr(nil)), terms(s(nil))) [2] a__sqr(0) -> 0 [1] a__sqr(s(terms(X6))) -> s(a__add(a__sqr(a__terms(mark(X6))), a__dbl(a__terms(mark(X6))))) [3] a__sqr(s(sqr(X7))) -> s(a__add(a__sqr(a__sqr(mark(X7))), a__dbl(a__sqr(mark(X7))))) [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(X8))) -> s(a__add(a__sqr(a__dbl(mark(X8))), a__dbl(a__dbl(mark(X8))))) [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(cons(X14, X24))) -> s(a__add(a__sqr(cons(mark(X14), X24)), a__dbl(cons(mark(X14), X24)))) [3] a__sqr(s(recip(X9))) -> s(a__add(a__sqr(recip(mark(X9))), a__dbl(recip(mark(X9))))) [3] a__sqr(s(s(X10))) -> s(a__add(a__sqr(s(mark(X10))), a__dbl(s(mark(X10))))) [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(X15))) -> s(s(a__dbl(a__terms(mark(X15))))) [2] a__dbl(s(sqr(X16))) -> s(s(a__dbl(a__sqr(mark(X16))))) [2] a__dbl(s(add(X17, X25))) -> s(s(a__dbl(a__add(mark(X17), mark(X25))))) [2] a__dbl(s(dbl(X18))) -> s(s(a__dbl(a__dbl(mark(X18))))) [2] a__dbl(s(first(X19, X26))) -> s(s(a__dbl(a__first(mark(X19), mark(X26))))) [2] a__dbl(s(cons(X110, X27))) -> s(s(a__dbl(cons(mark(X110), X27)))) [2] a__dbl(s(recip(X20))) -> s(s(a__dbl(recip(mark(X20))))) [2] a__dbl(s(s(X28))) -> s(s(a__dbl(s(mark(X28))))) [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] mark(terms(terms(X84))) -> a__terms(a__terms(mark(X84))) [2] mark(terms(sqr(X85))) -> a__terms(a__sqr(mark(X85))) [2] mark(terms(add(X144, X243))) -> a__terms(a__add(mark(X144), mark(X243))) [2] mark(terms(dbl(X86))) -> a__terms(a__dbl(mark(X86))) [2] mark(terms(first(X145, X244))) -> a__terms(a__first(mark(X145), mark(X244))) [2] mark(terms(cons(X146, X245))) -> a__terms(cons(mark(X146), X245)) [2] mark(terms(recip(X87))) -> a__terms(recip(mark(X87))) [2] mark(terms(s(X88))) -> a__terms(s(mark(X88))) [2] mark(terms(0)) -> a__terms(0) [2] mark(terms(nil)) -> a__terms(nil) [2] mark(sqr(terms(X89))) -> a__sqr(a__terms(mark(X89))) [2] mark(sqr(sqr(X90))) -> a__sqr(a__sqr(mark(X90))) [2] mark(sqr(add(X147, X246))) -> a__sqr(a__add(mark(X147), mark(X246))) [2] mark(sqr(dbl(X91))) -> a__sqr(a__dbl(mark(X91))) [2] mark(sqr(first(X148, X247))) -> a__sqr(a__first(mark(X148), mark(X247))) [2] mark(sqr(cons(X149, X248))) -> a__sqr(cons(mark(X149), X248)) [2] mark(sqr(recip(X92))) -> a__sqr(recip(mark(X92))) [2] mark(sqr(s(X93))) -> a__sqr(s(mark(X93))) [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(X285))) -> a__dbl(a__terms(mark(X285))) [2] mark(dbl(sqr(X286))) -> a__dbl(a__sqr(mark(X286))) [2] mark(dbl(add(X1109, X287))) -> a__dbl(a__add(mark(X1109), mark(X287))) [2] mark(dbl(dbl(X288))) -> a__dbl(a__dbl(mark(X288))) [2] mark(dbl(first(X1110, X289))) -> a__dbl(a__first(mark(X1110), mark(X289))) [2] mark(dbl(cons(X1111, X290))) -> a__dbl(cons(mark(X1111), X290)) [2] mark(dbl(recip(X291))) -> a__dbl(recip(mark(X291))) [2] mark(dbl(s(X292))) -> a__dbl(s(mark(X292))) [2] mark(dbl(0)) -> a__dbl(0) [2] mark(dbl(nil)) -> a__dbl(nil) [2] mark(first(X1, X2)) -> a__first(mark(X1), mark(X2)) [1] mark(cons(X1, X2)) -> cons(mark(X1), X2) [1] mark(recip(X)) -> recip(mark(X)) [1] mark(s(X)) -> s(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] The TRS has the following type information: a__terms :: recip:s:terms:cons:0:nil:first:sqr:add:dbl -> recip:s:terms:cons:0:nil:first:sqr:add:dbl cons :: recip:s:terms:cons:0:nil:first:sqr:add:dbl -> recip:s:terms:cons:0:nil:first:sqr:add:dbl -> recip:s:terms:cons:0:nil:first:sqr:add:dbl recip :: recip:s:terms:cons:0:nil:first:sqr:add:dbl -> recip:s:terms:cons:0:nil:first:sqr:add:dbl a__sqr :: recip:s:terms:cons:0:nil:first:sqr:add:dbl -> recip:s:terms:cons:0:nil:first:sqr:add:dbl mark :: recip:s:terms:cons:0:nil:first:sqr:add:dbl -> recip:s:terms:cons:0:nil:first:sqr:add:dbl terms :: recip:s:terms:cons:0:nil:first:sqr:add:dbl -> recip:s:terms:cons:0:nil:first:sqr:add:dbl s :: recip:s:terms:cons:0:nil:first:sqr:add:dbl -> recip:s:terms:cons:0:nil:first:sqr:add:dbl 0 :: recip:s:terms:cons:0:nil:first:sqr:add:dbl a__add :: recip:s:terms:cons:0:nil:first:sqr:add:dbl -> recip:s:terms:cons:0:nil:first:sqr:add:dbl -> recip:s:terms:cons:0:nil:first:sqr:add:dbl a__dbl :: recip:s:terms:cons:0:nil:first:sqr:add:dbl -> recip:s:terms:cons:0:nil:first:sqr:add:dbl a__first :: recip:s:terms:cons:0:nil:first:sqr:add:dbl -> recip:s:terms:cons:0:nil:first:sqr:add:dbl -> recip:s:terms:cons:0:nil:first:sqr:add:dbl nil :: recip:s:terms:cons:0:nil:first:sqr:add:dbl first :: recip:s:terms:cons:0:nil:first:sqr:add:dbl -> recip:s:terms:cons:0:nil:first:sqr:add:dbl -> recip:s:terms:cons:0:nil:first:sqr:add:dbl sqr :: recip:s:terms:cons:0:nil:first:sqr:add:dbl -> recip:s:terms:cons:0:nil:first:sqr:add:dbl add :: recip:s:terms:cons:0:nil:first:sqr:add:dbl -> recip:s:terms:cons:0:nil:first:sqr:add:dbl -> recip:s:terms:cons:0:nil:first:sqr:add:dbl dbl :: recip:s:terms:cons:0:nil:first:sqr:add:dbl -> recip:s:terms:cons:0:nil:first:sqr:add:dbl 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(X15)))) :|: z = 1 + (1 + X15), X15 >= 0 a__dbl(z) -{ 2 }-> 1 + (1 + a__dbl(a__sqr(mark(X16)))) :|: X16 >= 0, z = 1 + (1 + X16) a__dbl(z) -{ 2 }-> 1 + (1 + a__dbl(a__first(mark(X19), mark(X26)))) :|: z = 1 + (1 + X19 + X26), X26 >= 0, X19 >= 0 a__dbl(z) -{ 2 }-> 1 + (1 + a__dbl(a__dbl(mark(X18)))) :|: X18 >= 0, z = 1 + (1 + X18) a__dbl(z) -{ 2 }-> 1 + (1 + a__dbl(a__add(mark(X17), mark(X25)))) :|: X17 >= 0, z = 1 + (1 + X17 + X25), 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(X20))) :|: z = 1 + (1 + X20), X20 >= 0 a__dbl(z) -{ 2 }-> 1 + (1 + a__dbl(1 + mark(X28))) :|: X28 >= 0, z = 1 + (1 + X28) a__dbl(z) -{ 2 }-> 1 + (1 + a__dbl(1 + mark(X110) + X27)) :|: X110 >= 0, X27 >= 0, z = 1 + (1 + X110 + X27) a__first(z, z') -{ 1 }-> 1 :|: z' = X, X >= 0, z = 0 a__first(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__first(z, z') -{ 1 }-> 1 + mark(Y) + (1 + X + Z) :|: Z >= 0, z = 1 + X, Y >= 0, X >= 0, z' = 1 + Y + Z a__sqr(z) -{ 1 }-> 0 :|: z = 0 a__sqr(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__sqr(z) -{ 3 }-> 1 + a__add(a__sqr(a__terms(mark(X6))), a__dbl(a__terms(mark(X6)))) :|: X6 >= 0, z = 1 + (1 + X6) a__sqr(z) -{ 3 }-> 1 + a__add(a__sqr(a__sqr(mark(X7))), a__dbl(a__sqr(mark(X7)))) :|: X7 >= 0, z = 1 + (1 + X7) 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(X8))), a__dbl(a__dbl(mark(X8)))) :|: X8 >= 0, z = 1 + (1 + X8) 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(X10)), a__dbl(1 + mark(X10))) :|: z = 1 + (1 + X10), X10 >= 0 a__sqr(z) -{ 3 }-> 1 + a__add(a__sqr(1 + mark(X9)), a__dbl(1 + mark(X9))) :|: X9 >= 0, z = 1 + (1 + X9) 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__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(X4))) + (1 + (1 + (1 + X4))) :|: z = 1 + X4, X4 >= 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(X11) + X21)) + (1 + (1 + (1 + X11 + X21))) :|: X11 >= 0, X21 >= 0, z = 1 + X11 + X21 mark(z) -{ 2 }-> a__terms(a__terms(mark(X84))) :|: z = 1 + (1 + X84), X84 >= 0 mark(z) -{ 2 }-> a__terms(a__sqr(mark(X85))) :|: z = 1 + (1 + X85), X85 >= 0 mark(z) -{ 2 }-> a__terms(a__first(mark(X145), mark(X244))) :|: X244 >= 0, z = 1 + (1 + X145 + X244), X145 >= 0 mark(z) -{ 2 }-> a__terms(a__dbl(mark(X86))) :|: z = 1 + (1 + X86), X86 >= 0 mark(z) -{ 2 }-> a__terms(a__add(mark(X144), mark(X243))) :|: X243 >= 0, X144 >= 0, z = 1 + (1 + X144 + X243) 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(X87)) :|: X87 >= 0, z = 1 + (1 + X87) mark(z) -{ 2 }-> a__terms(1 + mark(X88)) :|: X88 >= 0, z = 1 + (1 + X88) mark(z) -{ 2 }-> a__terms(1 + mark(X146) + X245) :|: X146 >= 0, X245 >= 0, z = 1 + (1 + X146 + X245) mark(z) -{ 2 }-> a__sqr(a__terms(mark(X89))) :|: X89 >= 0, z = 1 + (1 + X89) mark(z) -{ 2 }-> a__sqr(a__sqr(mark(X90))) :|: z = 1 + (1 + X90), X90 >= 0 mark(z) -{ 2 }-> a__sqr(a__first(mark(X148), mark(X247))) :|: z = 1 + (1 + X148 + X247), X148 >= 0, X247 >= 0 mark(z) -{ 2 }-> a__sqr(a__dbl(mark(X91))) :|: X91 >= 0, z = 1 + (1 + X91) mark(z) -{ 2 }-> a__sqr(a__add(mark(X147), mark(X246))) :|: X147 >= 0, X246 >= 0, z = 1 + (1 + X147 + X246) 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(X92)) :|: X92 >= 0, z = 1 + (1 + X92) mark(z) -{ 2 }-> a__sqr(1 + mark(X93)) :|: z = 1 + (1 + X93), X93 >= 0 mark(z) -{ 2 }-> a__sqr(1 + mark(X149) + X248) :|: X149 >= 0, X248 >= 0, z = 1 + (1 + X149 + X248) 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(X285))) :|: z = 1 + (1 + X285), X285 >= 0 mark(z) -{ 2 }-> a__dbl(a__sqr(mark(X286))) :|: X286 >= 0, z = 1 + (1 + X286) mark(z) -{ 2 }-> a__dbl(a__first(mark(X1110), mark(X289))) :|: X1110 >= 0, X289 >= 0, z = 1 + (1 + X1110 + X289) mark(z) -{ 2 }-> a__dbl(a__dbl(mark(X288))) :|: z = 1 + (1 + X288), X288 >= 0 mark(z) -{ 2 }-> a__dbl(a__add(mark(X1109), mark(X287))) :|: z = 1 + (1 + X1109 + X287), X287 >= 0, X1109 >= 0 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(X291)) :|: X291 >= 0, z = 1 + (1 + X291) mark(z) -{ 2 }-> a__dbl(1 + mark(X292)) :|: X292 >= 0, z = 1 + (1 + X292) mark(z) -{ 2 }-> a__dbl(1 + mark(X1111) + X290) :|: X1111 >= 0, z = 1 + (1 + X1111 + X290), X290 >= 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 ---------------------------------------- (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__first(mark(X19), mark(X26)))) :|: z = 1 + (1 + X19 + X26), X26 >= 0, X19 >= 0 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(X17), mark(X25)))) :|: X17 >= 0, z = 1 + (1 + X17 + X25), 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(X110) + X27)) :|: X110 >= 0, X27 >= 0, z = 1 + (1 + X110 + X27) a__first(z, z') -{ 1 }-> 1 :|: z' >= 0, z = 0 a__first(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0 a__first(z, z') -{ 1 }-> 1 + mark(Y) + (1 + (z - 1) + Z) :|: Z >= 0, Y >= 0, z - 1 >= 0, z' = 1 + Y + Z a__sqr(z) -{ 1 }-> 0 :|: z = 0 a__sqr(z) -{ 1 }-> 1 + z :|: z >= 0 a__sqr(z) -{ 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__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__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__first(mark(X145), mark(X244))) :|: X244 >= 0, z = 1 + (1 + X145 + X244), X145 >= 0 mark(z) -{ 2 }-> a__terms(a__dbl(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__terms(a__add(mark(X144), mark(X243))) :|: X243 >= 0, X144 >= 0, z = 1 + (1 + X144 + X243) 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(X146) + X245) :|: X146 >= 0, X245 >= 0, z = 1 + (1 + X146 + X245) mark(z) -{ 2 }-> a__sqr(a__terms(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__sqr(a__sqr(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__sqr(a__first(mark(X148), mark(X247))) :|: z = 1 + (1 + X148 + X247), X148 >= 0, X247 >= 0 mark(z) -{ 2 }-> a__sqr(a__dbl(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__sqr(a__add(mark(X147), mark(X246))) :|: X147 >= 0, X246 >= 0, z = 1 + (1 + X147 + X246) 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(X149) + X248) :|: X149 >= 0, X248 >= 0, z = 1 + (1 + X149 + X248) mark(z) -{ 1 }-> a__first(mark(X1), mark(X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 2 }-> a__dbl(a__terms(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__dbl(a__sqr(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__dbl(a__first(mark(X1110), mark(X289))) :|: X1110 >= 0, X289 >= 0, z = 1 + (1 + X1110 + X289) mark(z) -{ 2 }-> a__dbl(a__dbl(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__dbl(a__add(mark(X1109), mark(X287))) :|: z = 1 + (1 + X1109 + X287), X287 >= 0, X1109 >= 0 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(X1111) + X290) :|: X1111 >= 0, z = 1 + (1 + X1111 + X290), X290 >= 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(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] mark(terms(X)) -> a__terms(mark(X)) [1] mark(sqr(X)) -> a__sqr(mark(X)) [1] mark(add(X1, X2)) -> a__add(mark(X1), mark(X2)) [1] mark(dbl(X)) -> a__dbl(mark(X)) [1] mark(first(X1, X2)) -> a__first(mark(X1), mark(X2)) [1] mark(cons(X1, X2)) -> cons(mark(X1), X2) [1] mark(recip(X)) -> recip(mark(X)) [1] mark(s(X)) -> s(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] The TRS has the following type information: a__terms :: recip:s:terms:cons:0:nil:first:sqr:add:dbl -> recip:s:terms:cons:0:nil:first:sqr:add:dbl cons :: recip:s:terms:cons:0:nil:first:sqr:add:dbl -> recip:s:terms:cons:0:nil:first:sqr:add:dbl -> recip:s:terms:cons:0:nil:first:sqr:add:dbl recip :: recip:s:terms:cons:0:nil:first:sqr:add:dbl -> recip:s:terms:cons:0:nil:first:sqr:add:dbl a__sqr :: recip:s:terms:cons:0:nil:first:sqr:add:dbl -> recip:s:terms:cons:0:nil:first:sqr:add:dbl mark :: recip:s:terms:cons:0:nil:first:sqr:add:dbl -> recip:s:terms:cons:0:nil:first:sqr:add:dbl terms :: recip:s:terms:cons:0:nil:first:sqr:add:dbl -> recip:s:terms:cons:0:nil:first:sqr:add:dbl s :: recip:s:terms:cons:0:nil:first:sqr:add:dbl -> recip:s:terms:cons:0:nil:first:sqr:add:dbl 0 :: recip:s:terms:cons:0:nil:first:sqr:add:dbl a__add :: recip:s:terms:cons:0:nil:first:sqr:add:dbl -> recip:s:terms:cons:0:nil:first:sqr:add:dbl -> recip:s:terms:cons:0:nil:first:sqr:add:dbl a__dbl :: recip:s:terms:cons:0:nil:first:sqr:add:dbl -> recip:s:terms:cons:0:nil:first:sqr:add:dbl a__first :: recip:s:terms:cons:0:nil:first:sqr:add:dbl -> recip:s:terms:cons:0:nil:first:sqr:add:dbl -> recip:s:terms:cons:0:nil:first:sqr:add:dbl nil :: recip:s:terms:cons:0:nil:first:sqr:add:dbl first :: recip:s:terms:cons:0:nil:first:sqr:add:dbl -> recip:s:terms:cons:0:nil:first:sqr:add:dbl -> recip:s:terms:cons:0:nil:first:sqr:add:dbl sqr :: recip:s:terms:cons:0:nil:first:sqr:add:dbl -> recip:s:terms:cons:0:nil:first:sqr:add:dbl add :: recip:s:terms:cons:0:nil:first:sqr:add:dbl -> recip:s:terms:cons:0:nil:first:sqr:add:dbl -> recip:s:terms:cons:0:nil:first:sqr:add:dbl dbl :: recip:s:terms:cons:0:nil:first:sqr:add:dbl -> recip:s:terms:cons:0:nil:first:sqr:add:dbl 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__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__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) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(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 MARK(terms(z0)) -> c16(A__TERMS(mark(z0)), MARK(z0)) MARK(sqr(z0)) -> c17(A__SQR(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c18(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c19(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c20(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c21(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c22(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(MARK(z0)) MARK(0) -> c26 MARK(nil) -> c27 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 MARK(terms(z0)) -> c16(A__TERMS(mark(z0)), MARK(z0)) MARK(sqr(z0)) -> c17(A__SQR(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c18(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c19(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c20(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c21(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c22(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(MARK(z0)) MARK(0) -> c26 MARK(nil) -> c27 K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1 Defined Pair Symbols: A__TERMS_1, A__SQR_1, A__DBL_1, A__ADD_2, A__FIRST_2, MARK_1 Compound Symbols: c_2, c1, c2, c3_3, c4_3, c5, c6, c7_2, c8, c9_1, c10_2, c11_2, c12, c13, c14_1, c15, c16_2, c17_2, c18_2, c19_2, c20_2, c21_2, c22_2, c23_1, c24_1, c25_1, c26, c27 ---------------------------------------- (23) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 10 trailing nodes: MARK(nil) -> c27 A__ADD(z0, z1) -> c12 A__DBL(z0) -> c8 A__FIRST(z0, z1) -> c15 A__DBL(0) -> c6 A__SQR(0) -> c2 A__TERMS(z0) -> c1 MARK(0) -> c26 A__FIRST(0, z0) -> c13 A__SQR(z0) -> c5 ---------------------------------------- (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) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(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)) MARK(terms(z0)) -> c16(A__TERMS(mark(z0)), MARK(z0)) MARK(sqr(z0)) -> c17(A__SQR(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c18(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c19(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c20(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c21(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c22(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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)) MARK(terms(z0)) -> c16(A__TERMS(mark(z0)), MARK(z0)) MARK(sqr(z0)) -> c17(A__SQR(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c18(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c19(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c20(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c21(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c22(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(MARK(z0)) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1 Defined Pair Symbols: A__TERMS_1, A__SQR_1, A__DBL_1, A__ADD_2, A__FIRST_2, MARK_1 Compound Symbols: c_2, c3_3, c4_3, c7_2, c9_1, c10_2, c11_2, c14_1, c16_2, c17_2, c18_2, c19_2, c20_2, c21_2, c22_2, c23_1, c24_1, c25_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(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) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(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)) MARK(terms(z0)) -> c16(A__TERMS(mark(z0)), MARK(z0)) MARK(sqr(z0)) -> c17(A__SQR(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c18(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c19(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c20(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c21(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c22(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(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)) MARK(terms(z0)) -> c16(A__TERMS(mark(z0)), MARK(z0)) MARK(sqr(z0)) -> c17(A__SQR(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c18(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c19(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c20(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c21(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c22(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(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, mark_1 Defined Pair Symbols: A__SQR_1, A__DBL_1, A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1 Compound Symbols: c3_3, c4_3, c7_2, c9_1, c10_2, c11_2, c14_1, c16_2, c17_2, c18_2, c19_2, c20_2, c21_2, c22_2, c23_1, c24_1, c25_1, c_2 ---------------------------------------- (27) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: A__TERMS(nil) -> c(A__SQR(nil), MARK(nil)) A__TERMS(0) -> c(A__SQR(0), MARK(0)) ---------------------------------------- (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) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(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)) MARK(terms(z0)) -> c16(A__TERMS(mark(z0)), MARK(z0)) MARK(sqr(z0)) -> c17(A__SQR(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c18(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c19(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c20(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c21(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c22(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(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)) MARK(terms(z0)) -> c16(A__TERMS(mark(z0)), MARK(z0)) MARK(sqr(z0)) -> c17(A__SQR(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c18(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c19(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c20(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c21(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c22(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(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, mark_1 Defined Pair Symbols: A__SQR_1, A__DBL_1, A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1 Compound Symbols: c3_3, c4_3, c7_2, c9_1, c10_2, c11_2, c14_1, c16_2, c17_2, c18_2, c19_2, c20_2, c21_2, c22_2, c23_1, c24_1, c25_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) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(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)) MARK(terms(z0)) -> c16(A__TERMS(mark(z0)), MARK(z0)) MARK(sqr(z0)) -> c17(A__SQR(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c18(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c19(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c20(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c21(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c22(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(s(z0)) -> c(A__SQR(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)) MARK(terms(z0)) -> c16(A__TERMS(mark(z0)), MARK(z0)) MARK(sqr(z0)) -> c17(A__SQR(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c18(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c19(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c20(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c21(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c22(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(s(z0)) -> c(A__SQR(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, mark_1 Defined Pair Symbols: A__SQR_1, A__DBL_1, A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1 Compound Symbols: c3_3, c4_3, c7_2, c9_1, c10_2, c11_2, c14_1, c16_2, c17_2, c18_2, c19_2, c20_2, c21_2, c22_2, c23_1, c24_1, c25_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(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(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) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(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)) MARK(terms(z0)) -> c16(A__TERMS(mark(z0)), MARK(z0)) MARK(sqr(z0)) -> c17(A__SQR(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c18(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c19(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c20(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c21(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c22(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(s(z0)) -> c(A__SQR(s(mark(z0))), 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(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(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)) MARK(terms(z0)) -> c16(A__TERMS(mark(z0)), MARK(z0)) MARK(sqr(z0)) -> c17(A__SQR(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c18(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c19(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c20(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c21(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c22(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(s(z0)) -> c(A__SQR(s(mark(z0))), 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(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(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, mark_1 Defined Pair Symbols: A__SQR_1, A__DBL_1, A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1 Compound Symbols: c4_3, c7_2, c9_1, c10_2, c11_2, c14_1, c16_2, c17_2, c18_2, c19_2, c20_2, c21_2, c22_2, c23_1, c24_1, c25_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) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(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)) MARK(terms(z0)) -> c16(A__TERMS(mark(z0)), MARK(z0)) MARK(sqr(z0)) -> c17(A__SQR(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c18(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c19(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c20(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c21(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c22(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(s(z0)) -> c(A__SQR(s(mark(z0))), 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(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(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)) MARK(terms(z0)) -> c16(A__TERMS(mark(z0)), MARK(z0)) MARK(sqr(z0)) -> c17(A__SQR(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c18(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c19(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c20(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c21(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c22(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(s(z0)) -> c(A__SQR(s(mark(z0))), 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(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(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, mark_1 Defined Pair Symbols: A__SQR_1, A__DBL_1, A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1 Compound Symbols: c4_3, c7_2, c9_1, c10_2, c11_2, c14_1, c16_2, c17_2, c18_2, c19_2, c20_2, c21_2, c22_2, c23_1, c24_1, c25_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(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> 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(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(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) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(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)) MARK(terms(z0)) -> c16(A__TERMS(mark(z0)), MARK(z0)) MARK(sqr(z0)) -> c17(A__SQR(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c18(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c19(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c20(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c21(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c22(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(s(z0)) -> c(A__SQR(s(mark(z0))), 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(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> 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(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(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)) MARK(terms(z0)) -> c16(A__TERMS(mark(z0)), MARK(z0)) MARK(sqr(z0)) -> c17(A__SQR(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c18(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c19(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c20(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c21(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c22(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(s(z0)) -> c(A__SQR(s(mark(z0))), 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(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> 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(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(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, mark_1 Defined Pair Symbols: A__DBL_1, A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1, A__SQR_1 Compound Symbols: c7_2, c9_1, c10_2, c11_2, c14_1, c16_2, c17_2, c18_2, c19_2, c20_2, c21_2, c22_2, c23_1, c24_1, c25_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) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(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)) MARK(terms(z0)) -> c16(A__TERMS(mark(z0)), MARK(z0)) MARK(sqr(z0)) -> c17(A__SQR(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c18(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c19(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c20(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c21(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c22(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(s(z0)) -> c(A__SQR(s(mark(z0))), 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(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(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)) MARK(terms(z0)) -> c16(A__TERMS(mark(z0)), MARK(z0)) MARK(sqr(z0)) -> c17(A__SQR(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c18(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c19(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c20(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c21(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c22(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(s(z0)) -> c(A__SQR(s(mark(z0))), 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(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(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, mark_1 Defined Pair Symbols: A__DBL_1, A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1, A__SQR_1 Compound Symbols: c7_2, c9_1, c10_2, c11_2, c14_1, c16_2, c17_2, c18_2, c19_2, c20_2, c21_2, c22_2, c23_1, c24_1, c25_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(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) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(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)) MARK(terms(z0)) -> c16(A__TERMS(mark(z0)), MARK(z0)) MARK(sqr(z0)) -> c17(A__SQR(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c18(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c19(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c20(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c21(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c22(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(s(z0)) -> c(A__SQR(s(mark(z0))), 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(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) 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)) MARK(terms(z0)) -> c16(A__TERMS(mark(z0)), MARK(z0)) MARK(sqr(z0)) -> c17(A__SQR(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c18(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c19(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c20(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c21(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c22(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(s(z0)) -> c(A__SQR(s(mark(z0))), 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(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) 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, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c10_2, c11_2, c14_1, c16_2, c17_2, c18_2, c19_2, c20_2, c21_2, c22_2, c23_1, c24_1, c25_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) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(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)) MARK(terms(z0)) -> c16(A__TERMS(mark(z0)), MARK(z0)) MARK(sqr(z0)) -> c17(A__SQR(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c18(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c19(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c20(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c21(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c22(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(s(z0)) -> c(A__SQR(s(mark(z0))), 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(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) 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)) MARK(terms(z0)) -> c16(A__TERMS(mark(z0)), MARK(z0)) MARK(sqr(z0)) -> c17(A__SQR(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c18(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c19(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c20(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c21(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c22(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(s(z0)) -> c(A__SQR(s(mark(z0))), 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(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) 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, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c10_2, c11_2, c14_1, c16_2, c17_2, c18_2, c19_2, c20_2, c21_2, c22_2, c23_1, c24_1, c25_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) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(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)) MARK(terms(z0)) -> c16(A__TERMS(mark(z0)), MARK(z0)) MARK(sqr(z0)) -> c17(A__SQR(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c18(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c19(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c20(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c21(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c22(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(s(z0)) -> c(A__SQR(s(mark(z0))), 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(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(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)) MARK(terms(z0)) -> c16(A__TERMS(mark(z0)), MARK(z0)) MARK(sqr(z0)) -> c17(A__SQR(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c18(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c19(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c20(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c21(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c22(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(s(z0)) -> c(A__SQR(s(mark(z0))), 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(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(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, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c10_2, c11_2, c14_1, c16_2, c17_2, c18_2, c19_2, c20_2, c21_2, c22_2, c23_1, c24_1, c25_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), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) 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) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(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)) MARK(terms(z0)) -> c16(A__TERMS(mark(z0)), MARK(z0)) MARK(sqr(z0)) -> c17(A__SQR(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c18(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c19(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c20(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c21(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c22(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(s(z0)) -> c(A__SQR(s(mark(z0))), 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(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) 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)) MARK(terms(z0)) -> c16(A__TERMS(mark(z0)), MARK(z0)) MARK(sqr(z0)) -> c17(A__SQR(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c18(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c19(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c20(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c21(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c22(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(s(z0)) -> c(A__SQR(s(mark(z0))), 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(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) 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, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c11_2, c14_1, c16_2, c17_2, c18_2, c19_2, c20_2, c21_2, c22_2, c23_1, c24_1, c25_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) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(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)) MARK(terms(z0)) -> c16(A__TERMS(mark(z0)), MARK(z0)) MARK(sqr(z0)) -> c17(A__SQR(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c18(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c19(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c20(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c21(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c22(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(s(z0)) -> c(A__SQR(s(mark(z0))), 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(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) 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)) MARK(terms(z0)) -> c16(A__TERMS(mark(z0)), MARK(z0)) MARK(sqr(z0)) -> c17(A__SQR(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c18(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c19(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c20(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c21(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c22(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(s(z0)) -> c(A__SQR(s(mark(z0))), 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(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) 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, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c11_2, c14_1, c16_2, c17_2, c18_2, c19_2, c20_2, c21_2, c22_2, c23_1, c24_1, c25_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) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(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)) MARK(terms(z0)) -> c16(A__TERMS(mark(z0)), MARK(z0)) MARK(sqr(z0)) -> c17(A__SQR(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c18(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c19(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c20(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c21(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c22(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(s(z0)) -> c(A__SQR(s(mark(z0))), 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(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(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)) MARK(terms(z0)) -> c16(A__TERMS(mark(z0)), MARK(z0)) MARK(sqr(z0)) -> c17(A__SQR(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c18(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c19(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c20(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c21(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c22(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(s(z0)) -> c(A__SQR(s(mark(z0))), 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(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(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, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c11_2, c14_1, c16_2, c17_2, c18_2, c19_2, c20_2, c21_2, c22_2, c23_1, c24_1, c25_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), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(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(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) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(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)) MARK(terms(z0)) -> c16(A__TERMS(mark(z0)), MARK(z0)) MARK(sqr(z0)) -> c17(A__SQR(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c18(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c19(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c20(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c21(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c22(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(s(z0)) -> c(A__SQR(s(mark(z0))), 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(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(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(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)) MARK(terms(z0)) -> c16(A__TERMS(mark(z0)), MARK(z0)) MARK(sqr(z0)) -> c17(A__SQR(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c18(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c19(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c20(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c21(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c22(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(s(z0)) -> c(A__SQR(s(mark(z0))), 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(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(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(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, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c16_2, c17_2, c18_2, c19_2, c20_2, c21_2, c22_2, c23_1, c24_1, c25_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) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(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)) MARK(terms(z0)) -> c16(A__TERMS(mark(z0)), MARK(z0)) MARK(sqr(z0)) -> c17(A__SQR(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c18(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c19(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c20(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c21(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c22(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(s(z0)) -> c(A__SQR(s(mark(z0))), 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(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(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)) MARK(terms(z0)) -> c16(A__TERMS(mark(z0)), MARK(z0)) MARK(sqr(z0)) -> c17(A__SQR(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c18(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c19(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c20(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c21(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c22(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(s(z0)) -> c(A__SQR(s(mark(z0))), 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(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(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, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c16_2, c17_2, c18_2, c19_2, c20_2, c21_2, c22_2, c23_1, c24_1, c25_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 MARK(terms(z0)) -> c16(A__TERMS(mark(z0)), MARK(z0)) by MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(terms(0)) -> c16(A__TERMS(0), MARK(0)) MARK(terms(nil)) -> c16(A__TERMS(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) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(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)) MARK(sqr(z0)) -> c17(A__SQR(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c18(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c19(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c20(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c21(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c22(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(s(z0)) -> c(A__SQR(s(mark(z0))), 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(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(terms(0)) -> c16(A__TERMS(0), MARK(0)) MARK(terms(nil)) -> c16(A__TERMS(nil), MARK(nil)) S tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) MARK(sqr(z0)) -> c17(A__SQR(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c18(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c19(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c20(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c21(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c22(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(s(z0)) -> c(A__SQR(s(mark(z0))), 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(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(terms(0)) -> c16(A__TERMS(0), MARK(0)) MARK(terms(nil)) -> c16(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, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c17_2, c18_2, c19_2, c20_2, c21_2, c22_2, c23_1, c24_1, c25_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, c16_2 ---------------------------------------- (57) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(terms(0)) -> c16(A__TERMS(0), MARK(0)) MARK(terms(nil)) -> c16(A__TERMS(nil), MARK(nil)) ---------------------------------------- (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) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(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)) MARK(sqr(z0)) -> c17(A__SQR(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c18(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c19(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c20(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c21(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c22(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(s(z0)) -> c(A__SQR(s(mark(z0))), 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(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(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)) MARK(sqr(z0)) -> c17(A__SQR(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c18(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c19(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c20(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c21(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c22(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(s(z0)) -> c(A__SQR(s(mark(z0))), 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(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(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, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c17_2, c18_2, c19_2, c20_2, c21_2, c22_2, c23_1, c24_1, c25_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, c16_2 ---------------------------------------- (59) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(sqr(z0)) -> c17(A__SQR(mark(z0)), MARK(z0)) by MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(cons(z0, z1))) -> c17(A__SQR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(A__SQR(recip(mark(z0))), MARK(recip(z0))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(0)) -> c17(A__SQR(0), MARK(0)) MARK(sqr(nil)) -> c17(A__SQR(nil), MARK(nil)) ---------------------------------------- (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) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(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)) MARK(add(z0, z1)) -> c18(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c19(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c20(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c21(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c22(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(s(z0)) -> c(A__SQR(s(mark(z0))), 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(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(cons(z0, z1))) -> c17(A__SQR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(A__SQR(recip(mark(z0))), MARK(recip(z0))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(0)) -> c17(A__SQR(0), MARK(0)) MARK(sqr(nil)) -> c17(A__SQR(nil), MARK(nil)) S tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) MARK(add(z0, z1)) -> c18(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c19(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c20(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c21(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c22(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(s(z0)) -> c(A__SQR(s(mark(z0))), 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(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(cons(z0, z1))) -> c17(A__SQR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(A__SQR(recip(mark(z0))), MARK(recip(z0))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(0)) -> c17(A__SQR(0), MARK(0)) MARK(sqr(nil)) -> c17(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, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c18_2, c19_2, c20_2, c21_2, c22_2, c23_1, c24_1, c25_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, c16_2, c17_2 ---------------------------------------- (61) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(sqr(nil)) -> c17(A__SQR(nil), MARK(nil)) MARK(sqr(0)) -> c17(A__SQR(0), MARK(0)) ---------------------------------------- (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) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(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)) MARK(add(z0, z1)) -> c18(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c19(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c20(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c21(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c22(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(s(z0)) -> c(A__SQR(s(mark(z0))), 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(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(cons(z0, z1))) -> c17(A__SQR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(A__SQR(recip(mark(z0))), MARK(recip(z0))) MARK(sqr(s(z0))) -> c17(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)) MARK(add(z0, z1)) -> c18(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c19(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c20(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c21(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c22(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(s(z0)) -> c(A__SQR(s(mark(z0))), 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(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(cons(z0, z1))) -> c17(A__SQR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(A__SQR(recip(mark(z0))), MARK(recip(z0))) MARK(sqr(s(z0))) -> c17(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, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c18_2, c19_2, c20_2, c21_2, c22_2, c23_1, c24_1, c25_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, c16_2, c17_2 ---------------------------------------- (63) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (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) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(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)) MARK(add(z0, z1)) -> c18(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c19(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c20(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c21(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c22(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(s(z0)) -> c(A__SQR(s(mark(z0))), 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(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) S tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) MARK(add(z0, z1)) -> c18(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c19(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c20(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c21(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c22(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(s(z0)) -> c(A__SQR(s(mark(z0))), 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(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c18_2, c19_2, c20_2, c21_2, c22_2, c23_1, c24_1, c25_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, c16_2, c17_2, c17_1 ---------------------------------------- (65) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(add(z0, z1)) -> c18(A__ADD(mark(z0), mark(z1)), MARK(z0)) by MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c18(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c18(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c18(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c18(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c18(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c18(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c18(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c18(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c18(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c18(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), x1)) -> c18(A__ADD(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c18(A__ADD(recip(mark(z0)), mark(x1)), MARK(recip(z0))) MARK(add(s(z0), x1)) -> c18(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c18(A__ADD(0, mark(x1)), MARK(0)) MARK(add(nil, x1)) -> c18(A__ADD(nil, mark(x1)), MARK(nil)) ---------------------------------------- (66) Obligation: Complexity Dependency Tuples Problem Rules: a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0) -> 0 a__sqr(s(z0)) -> s(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) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(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)) MARK(add(z0, z1)) -> c19(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c20(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c21(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c22(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(s(z0)) -> c(A__SQR(s(mark(z0))), 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(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c18(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c18(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c18(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c18(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c18(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c18(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c18(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c18(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c18(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c18(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), x1)) -> c18(A__ADD(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c18(A__ADD(recip(mark(z0)), mark(x1)), MARK(recip(z0))) MARK(add(s(z0), x1)) -> c18(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c18(A__ADD(0, mark(x1)), MARK(0)) MARK(add(nil, x1)) -> c18(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)) MARK(add(z0, z1)) -> c19(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c20(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c21(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c22(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(s(z0)) -> c(A__SQR(s(mark(z0))), 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(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c18(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c18(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c18(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c18(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c18(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c18(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c18(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c18(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c18(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c18(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), x1)) -> c18(A__ADD(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c18(A__ADD(recip(mark(z0)), mark(x1)), MARK(recip(z0))) MARK(add(s(z0), x1)) -> c18(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c18(A__ADD(0, mark(x1)), MARK(0)) MARK(add(nil, x1)) -> c18(A__ADD(nil, mark(x1)), MARK(nil)) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c19_2, c20_2, c21_2, c22_2, c23_1, c24_1, c25_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, c16_2, c17_2, c17_1, c18_2 ---------------------------------------- (67) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(add(nil, x1)) -> c18(A__ADD(nil, mark(x1)), 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) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(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)) MARK(add(z0, z1)) -> c19(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c20(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c21(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c22(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(s(z0)) -> c(A__SQR(s(mark(z0))), 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(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c18(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c18(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c18(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c18(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c18(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c18(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c18(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c18(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c18(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c18(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), x1)) -> c18(A__ADD(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c18(A__ADD(recip(mark(z0)), mark(x1)), MARK(recip(z0))) MARK(add(s(z0), x1)) -> c18(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c18(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)) MARK(add(z0, z1)) -> c19(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c20(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c21(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c22(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(s(z0)) -> c(A__SQR(s(mark(z0))), 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(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c18(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c18(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c18(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c18(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c18(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c18(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c18(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c18(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c18(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c18(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), x1)) -> c18(A__ADD(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c18(A__ADD(recip(mark(z0)), mark(x1)), MARK(recip(z0))) MARK(add(s(z0), x1)) -> c18(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c18(A__ADD(0, mark(x1)), MARK(0)) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c19_2, c20_2, c21_2, c22_2, c23_1, c24_1, c25_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, c16_2, c17_2, c17_1, c18_2 ---------------------------------------- (69) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 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) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(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)) MARK(add(z0, z1)) -> c19(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c20(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c21(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c22(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(s(z0)) -> c(A__SQR(s(mark(z0))), 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(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c18(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c18(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c18(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c18(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c18(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c18(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c18(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c18(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c18(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c18(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(s(z0), x1)) -> c18(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c18(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c18(MARK(recip(z0))) MARK(add(0, x1)) -> c18(A__ADD(0, mark(x1))) S tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) MARK(add(z0, z1)) -> c19(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c20(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c21(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c22(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(s(z0)) -> c(A__SQR(s(mark(z0))), 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(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c18(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c18(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c18(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c18(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c18(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c18(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c18(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c18(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c18(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c18(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(s(z0), x1)) -> c18(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c18(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c18(MARK(recip(z0))) MARK(add(0, x1)) -> c18(A__ADD(0, mark(x1))) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c19_2, c20_2, c21_2, c22_2, c23_1, c24_1, c25_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, c16_2, c17_2, c17_1, c18_2, c18_1 ---------------------------------------- (71) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(add(z0, z1)) -> c19(A__ADD(mark(z0), mark(z1)), MARK(z1)) by MARK(add(x0, terms(z0))) -> c19(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c19(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c19(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c19(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c19(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c19(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c19(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c19(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(x0, 0)) -> c19(A__ADD(mark(x0), 0), MARK(0)) MARK(add(x0, nil)) -> c19(A__ADD(mark(x0), nil), MARK(nil)) MARK(add(terms(z0), x1)) -> c19(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c19(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c19(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c19(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c19(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(cons(z0, z1), x1)) -> c19(A__ADD(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(add(recip(z0), x1)) -> c19(A__ADD(recip(mark(z0)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c19(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c19(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(nil, x1)) -> c19(A__ADD(nil, mark(x1)), MARK(x1)) ---------------------------------------- (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) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(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)) MARK(dbl(z0)) -> c20(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c21(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c22(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(s(z0)) -> c(A__SQR(s(mark(z0))), 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(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c18(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c18(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c18(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c18(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c18(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c18(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c18(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c18(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c18(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c18(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(s(z0), x1)) -> c18(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c18(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c18(MARK(recip(z0))) MARK(add(0, x1)) -> c18(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c19(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c19(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c19(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c19(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c19(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c19(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c19(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c19(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(x0, 0)) -> c19(A__ADD(mark(x0), 0), MARK(0)) MARK(add(x0, nil)) -> c19(A__ADD(mark(x0), nil), MARK(nil)) MARK(add(terms(z0), x1)) -> c19(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c19(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c19(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c19(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c19(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(cons(z0, z1), x1)) -> c19(A__ADD(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(add(recip(z0), x1)) -> c19(A__ADD(recip(mark(z0)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c19(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c19(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(nil, x1)) -> c19(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)) MARK(dbl(z0)) -> c20(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c21(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c22(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(s(z0)) -> c(A__SQR(s(mark(z0))), 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(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c18(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c18(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c18(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c18(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c18(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c18(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c18(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c18(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c18(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c18(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(s(z0), x1)) -> c18(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c18(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c18(MARK(recip(z0))) MARK(add(0, x1)) -> c18(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c19(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c19(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c19(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c19(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c19(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c19(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c19(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c19(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(x0, 0)) -> c19(A__ADD(mark(x0), 0), MARK(0)) MARK(add(x0, nil)) -> c19(A__ADD(mark(x0), nil), MARK(nil)) MARK(add(terms(z0), x1)) -> c19(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c19(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c19(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c19(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c19(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(cons(z0, z1), x1)) -> c19(A__ADD(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(add(recip(z0), x1)) -> c19(A__ADD(recip(mark(z0)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c19(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c19(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(nil, x1)) -> c19(A__ADD(nil, mark(x1)), MARK(x1)) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c20_2, c21_2, c22_2, c23_1, c24_1, c25_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, c16_2, c17_2, c17_1, c18_2, c18_1, c19_2 ---------------------------------------- (73) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 5 trailing tuple parts ---------------------------------------- (74) Obligation: Complexity Dependency Tuples Problem Rules: a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0) -> 0 a__sqr(s(z0)) -> s(a__add(a__sqr(mark(z0)), a__dbl(mark(z0)))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(a__dbl(mark(z0)))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(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)) MARK(dbl(z0)) -> c20(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c21(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c22(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(s(z0)) -> c(A__SQR(s(mark(z0))), 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(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c18(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c18(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c18(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c18(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c18(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c18(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c18(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c18(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c18(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c18(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(s(z0), x1)) -> c18(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c18(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c18(MARK(recip(z0))) MARK(add(0, x1)) -> c18(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c19(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c19(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c19(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c19(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c19(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c19(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c19(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c19(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c19(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c19(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c19(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c19(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c19(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c19(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c19(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c19(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c19(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c19(MARK(x1)) MARK(add(recip(z0), x1)) -> c19(MARK(x1)) MARK(add(nil, x1)) -> c19(MARK(x1)) S tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) MARK(dbl(z0)) -> c20(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c21(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c22(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(s(z0)) -> c(A__SQR(s(mark(z0))), 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(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c18(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c18(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c18(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c18(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c18(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c18(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c18(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c18(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c18(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c18(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(s(z0), x1)) -> c18(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c18(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c18(MARK(recip(z0))) MARK(add(0, x1)) -> c18(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c19(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c19(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c19(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c19(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c19(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c19(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c19(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c19(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c19(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c19(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c19(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c19(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c19(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c19(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c19(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c19(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c19(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c19(MARK(x1)) MARK(add(recip(z0), x1)) -> c19(MARK(x1)) MARK(add(nil, x1)) -> c19(MARK(x1)) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c20_2, c21_2, c22_2, c23_1, c24_1, c25_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, c16_2, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1 ---------------------------------------- (75) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(dbl(z0)) -> c20(A__DBL(mark(z0)), MARK(z0)) by MARK(dbl(terms(z0))) -> c20(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c20(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c20(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c20(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c20(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(cons(z0, z1))) -> c20(A__DBL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c20(A__DBL(recip(mark(z0))), MARK(recip(z0))) MARK(dbl(s(z0))) -> c20(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(0)) -> c20(A__DBL(0), MARK(0)) MARK(dbl(nil)) -> c20(A__DBL(nil), MARK(nil)) ---------------------------------------- (76) Obligation: Complexity Dependency Tuples Problem Rules: a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0) -> 0 a__sqr(s(z0)) -> s(a__add(a__sqr(mark(z0)), a__dbl(mark(z0)))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(a__dbl(mark(z0)))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(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)) MARK(first(z0, z1)) -> c21(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c22(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(s(z0)) -> c(A__SQR(s(mark(z0))), 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(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c18(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c18(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c18(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c18(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c18(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c18(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c18(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c18(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c18(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c18(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(s(z0), x1)) -> c18(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c18(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c18(MARK(recip(z0))) MARK(add(0, x1)) -> c18(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c19(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c19(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c19(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c19(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c19(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c19(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c19(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c19(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c19(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c19(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c19(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c19(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c19(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c19(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c19(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c19(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c19(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c19(MARK(x1)) MARK(add(recip(z0), x1)) -> c19(MARK(x1)) MARK(add(nil, x1)) -> c19(MARK(x1)) MARK(dbl(terms(z0))) -> c20(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c20(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c20(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c20(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c20(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(cons(z0, z1))) -> c20(A__DBL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c20(A__DBL(recip(mark(z0))), MARK(recip(z0))) MARK(dbl(s(z0))) -> c20(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(0)) -> c20(A__DBL(0), MARK(0)) MARK(dbl(nil)) -> c20(A__DBL(nil), MARK(nil)) S tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) MARK(first(z0, z1)) -> c21(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c22(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(s(z0)) -> c(A__SQR(s(mark(z0))), 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(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c18(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c18(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c18(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c18(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c18(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c18(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c18(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c18(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c18(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c18(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(s(z0), x1)) -> c18(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c18(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c18(MARK(recip(z0))) MARK(add(0, x1)) -> c18(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c19(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c19(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c19(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c19(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c19(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c19(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c19(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c19(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c19(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c19(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c19(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c19(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c19(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c19(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c19(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c19(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c19(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c19(MARK(x1)) MARK(add(recip(z0), x1)) -> c19(MARK(x1)) MARK(add(nil, x1)) -> c19(MARK(x1)) MARK(dbl(terms(z0))) -> c20(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c20(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c20(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c20(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c20(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(cons(z0, z1))) -> c20(A__DBL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c20(A__DBL(recip(mark(z0))), MARK(recip(z0))) MARK(dbl(s(z0))) -> c20(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(0)) -> c20(A__DBL(0), MARK(0)) MARK(dbl(nil)) -> c20(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, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c21_2, c22_2, c23_1, c24_1, c25_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, c16_2, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2 ---------------------------------------- (77) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(dbl(0)) -> c20(A__DBL(0), MARK(0)) MARK(dbl(nil)) -> c20(A__DBL(nil), MARK(nil)) ---------------------------------------- (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) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(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)) MARK(first(z0, z1)) -> c21(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c22(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(s(z0)) -> c(A__SQR(s(mark(z0))), 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(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c18(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c18(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c18(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c18(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c18(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c18(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c18(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c18(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c18(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c18(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(s(z0), x1)) -> c18(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c18(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c18(MARK(recip(z0))) MARK(add(0, x1)) -> c18(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c19(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c19(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c19(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c19(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c19(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c19(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c19(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c19(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c19(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c19(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c19(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c19(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c19(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c19(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c19(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c19(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c19(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c19(MARK(x1)) MARK(add(recip(z0), x1)) -> c19(MARK(x1)) MARK(add(nil, x1)) -> c19(MARK(x1)) MARK(dbl(terms(z0))) -> c20(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c20(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c20(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c20(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c20(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(cons(z0, z1))) -> c20(A__DBL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c20(A__DBL(recip(mark(z0))), MARK(recip(z0))) MARK(dbl(s(z0))) -> c20(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)) MARK(first(z0, z1)) -> c21(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c22(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(s(z0)) -> c(A__SQR(s(mark(z0))), 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(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c18(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c18(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c18(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c18(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c18(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c18(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c18(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c18(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c18(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c18(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(s(z0), x1)) -> c18(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c18(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c18(MARK(recip(z0))) MARK(add(0, x1)) -> c18(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c19(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c19(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c19(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c19(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c19(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c19(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c19(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c19(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c19(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c19(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c19(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c19(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c19(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c19(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c19(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c19(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c19(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c19(MARK(x1)) MARK(add(recip(z0), x1)) -> c19(MARK(x1)) MARK(add(nil, x1)) -> c19(MARK(x1)) MARK(dbl(terms(z0))) -> c20(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c20(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c20(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c20(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c20(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(cons(z0, z1))) -> c20(A__DBL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c20(A__DBL(recip(mark(z0))), MARK(recip(z0))) MARK(dbl(s(z0))) -> c20(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, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c21_2, c22_2, c23_1, c24_1, c25_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, c16_2, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2 ---------------------------------------- (79) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 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) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(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)) MARK(first(z0, z1)) -> c21(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c22(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(s(z0)) -> c(A__SQR(s(mark(z0))), 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(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c18(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c18(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c18(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c18(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c18(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c18(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c18(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c18(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c18(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c18(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(s(z0), x1)) -> c18(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c18(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c18(MARK(recip(z0))) MARK(add(0, x1)) -> c18(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c19(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c19(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c19(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c19(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c19(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c19(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c19(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c19(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c19(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c19(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c19(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c19(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c19(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c19(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c19(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c19(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c19(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c19(MARK(x1)) MARK(add(recip(z0), x1)) -> c19(MARK(x1)) MARK(add(nil, x1)) -> c19(MARK(x1)) MARK(dbl(terms(z0))) -> c20(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c20(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c20(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c20(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c20(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(s(z0))) -> c20(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c20(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c20(MARK(recip(z0))) S tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) MARK(first(z0, z1)) -> c21(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c22(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(s(z0)) -> c(A__SQR(s(mark(z0))), 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(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c18(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c18(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c18(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c18(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c18(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c18(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c18(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c18(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c18(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c18(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(s(z0), x1)) -> c18(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c18(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c18(MARK(recip(z0))) MARK(add(0, x1)) -> c18(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c19(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c19(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c19(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c19(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c19(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c19(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c19(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c19(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c19(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c19(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c19(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c19(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c19(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c19(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c19(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c19(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c19(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c19(MARK(x1)) MARK(add(recip(z0), x1)) -> c19(MARK(x1)) MARK(add(nil, x1)) -> c19(MARK(x1)) MARK(dbl(terms(z0))) -> c20(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c20(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c20(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c20(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c20(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(s(z0))) -> c20(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c20(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c20(MARK(recip(z0))) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c21_2, c22_2, c23_1, c24_1, c25_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, c16_2, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1 ---------------------------------------- (81) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(first(z0, z1)) -> c21(A__FIRST(mark(z0), mark(z1)), MARK(z0)) by MARK(first(x0, terms(z0))) -> c21(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c21(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c21(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c21(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c21(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c21(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(x0, recip(z0))) -> c21(A__FIRST(mark(x0), recip(mark(z0))), MARK(x0)) MARK(first(x0, s(z0))) -> c21(A__FIRST(mark(x0), s(mark(z0))), MARK(x0)) MARK(first(x0, 0)) -> c21(A__FIRST(mark(x0), 0), MARK(x0)) MARK(first(x0, nil)) -> c21(A__FIRST(mark(x0), nil), MARK(x0)) MARK(first(terms(z0), x1)) -> c21(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c21(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c21(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c21(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c21(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(cons(z0, z1), x1)) -> c21(A__FIRST(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c21(A__FIRST(recip(mark(z0)), mark(x1)), MARK(recip(z0))) MARK(first(s(z0), x1)) -> c21(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(0, x1)) -> c21(A__FIRST(0, mark(x1)), MARK(0)) MARK(first(nil, x1)) -> c21(A__FIRST(nil, mark(x1)), 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) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(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)) MARK(first(z0, z1)) -> c22(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(s(z0)) -> c(A__SQR(s(mark(z0))), 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(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c18(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c18(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c18(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c18(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c18(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c18(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c18(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c18(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c18(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c18(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(s(z0), x1)) -> c18(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c18(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c18(MARK(recip(z0))) MARK(add(0, x1)) -> c18(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c19(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c19(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c19(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c19(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c19(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c19(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c19(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c19(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c19(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c19(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c19(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c19(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c19(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c19(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c19(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c19(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c19(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c19(MARK(x1)) MARK(add(recip(z0), x1)) -> c19(MARK(x1)) MARK(add(nil, x1)) -> c19(MARK(x1)) MARK(dbl(terms(z0))) -> c20(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c20(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c20(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c20(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c20(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(s(z0))) -> c20(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c20(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c20(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c21(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c21(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c21(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c21(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c21(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c21(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(x0, recip(z0))) -> c21(A__FIRST(mark(x0), recip(mark(z0))), MARK(x0)) MARK(first(x0, s(z0))) -> c21(A__FIRST(mark(x0), s(mark(z0))), MARK(x0)) MARK(first(x0, 0)) -> c21(A__FIRST(mark(x0), 0), MARK(x0)) MARK(first(x0, nil)) -> c21(A__FIRST(mark(x0), nil), MARK(x0)) MARK(first(terms(z0), x1)) -> c21(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c21(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c21(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c21(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c21(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(cons(z0, z1), x1)) -> c21(A__FIRST(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c21(A__FIRST(recip(mark(z0)), mark(x1)), MARK(recip(z0))) MARK(first(s(z0), x1)) -> c21(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(0, x1)) -> c21(A__FIRST(0, mark(x1)), MARK(0)) MARK(first(nil, x1)) -> c21(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)) MARK(first(z0, z1)) -> c22(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(s(z0)) -> c(A__SQR(s(mark(z0))), 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(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c18(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c18(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c18(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c18(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c18(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c18(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c18(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c18(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c18(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c18(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(s(z0), x1)) -> c18(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c18(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c18(MARK(recip(z0))) MARK(add(0, x1)) -> c18(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c19(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c19(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c19(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c19(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c19(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c19(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c19(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c19(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c19(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c19(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c19(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c19(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c19(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c19(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c19(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c19(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c19(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c19(MARK(x1)) MARK(add(recip(z0), x1)) -> c19(MARK(x1)) MARK(add(nil, x1)) -> c19(MARK(x1)) MARK(dbl(terms(z0))) -> c20(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c20(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c20(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c20(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c20(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(s(z0))) -> c20(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c20(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c20(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c21(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c21(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c21(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c21(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c21(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c21(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(x0, recip(z0))) -> c21(A__FIRST(mark(x0), recip(mark(z0))), MARK(x0)) MARK(first(x0, s(z0))) -> c21(A__FIRST(mark(x0), s(mark(z0))), MARK(x0)) MARK(first(x0, 0)) -> c21(A__FIRST(mark(x0), 0), MARK(x0)) MARK(first(x0, nil)) -> c21(A__FIRST(mark(x0), nil), MARK(x0)) MARK(first(terms(z0), x1)) -> c21(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c21(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c21(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c21(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c21(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(cons(z0, z1), x1)) -> c21(A__FIRST(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c21(A__FIRST(recip(mark(z0)), mark(x1)), MARK(recip(z0))) MARK(first(s(z0), x1)) -> c21(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(0, x1)) -> c21(A__FIRST(0, mark(x1)), MARK(0)) MARK(first(nil, x1)) -> c21(A__FIRST(nil, mark(x1)), MARK(nil)) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c22_2, c23_1, c24_1, c25_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, c16_2, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2 ---------------------------------------- (83) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(first(nil, x1)) -> c21(A__FIRST(nil, mark(x1)), MARK(nil)) MARK(first(0, x1)) -> c21(A__FIRST(0, mark(x1)), MARK(0)) ---------------------------------------- (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) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(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)) MARK(first(z0, z1)) -> c22(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(s(z0)) -> c(A__SQR(s(mark(z0))), 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(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c18(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c18(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c18(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c18(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c18(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c18(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c18(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c18(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c18(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c18(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(s(z0), x1)) -> c18(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c18(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c18(MARK(recip(z0))) MARK(add(0, x1)) -> c18(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c19(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c19(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c19(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c19(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c19(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c19(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c19(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c19(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c19(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c19(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c19(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c19(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c19(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c19(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c19(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c19(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c19(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c19(MARK(x1)) MARK(add(recip(z0), x1)) -> c19(MARK(x1)) MARK(add(nil, x1)) -> c19(MARK(x1)) MARK(dbl(terms(z0))) -> c20(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c20(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c20(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c20(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c20(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(s(z0))) -> c20(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c20(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c20(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c21(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c21(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c21(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c21(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c21(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c21(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(x0, recip(z0))) -> c21(A__FIRST(mark(x0), recip(mark(z0))), MARK(x0)) MARK(first(x0, s(z0))) -> c21(A__FIRST(mark(x0), s(mark(z0))), MARK(x0)) MARK(first(x0, 0)) -> c21(A__FIRST(mark(x0), 0), MARK(x0)) MARK(first(x0, nil)) -> c21(A__FIRST(mark(x0), nil), MARK(x0)) MARK(first(terms(z0), x1)) -> c21(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c21(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c21(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c21(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c21(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(cons(z0, z1), x1)) -> c21(A__FIRST(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c21(A__FIRST(recip(mark(z0)), mark(x1)), MARK(recip(z0))) MARK(first(s(z0), x1)) -> c21(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)) MARK(first(z0, z1)) -> c22(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(s(z0)) -> c(A__SQR(s(mark(z0))), 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(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c18(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c18(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c18(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c18(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c18(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c18(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c18(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c18(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c18(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c18(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(s(z0), x1)) -> c18(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c18(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c18(MARK(recip(z0))) MARK(add(0, x1)) -> c18(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c19(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c19(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c19(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c19(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c19(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c19(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c19(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c19(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c19(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c19(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c19(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c19(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c19(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c19(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c19(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c19(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c19(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c19(MARK(x1)) MARK(add(recip(z0), x1)) -> c19(MARK(x1)) MARK(add(nil, x1)) -> c19(MARK(x1)) MARK(dbl(terms(z0))) -> c20(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c20(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c20(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c20(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c20(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(s(z0))) -> c20(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c20(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c20(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c21(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c21(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c21(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c21(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c21(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c21(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(x0, recip(z0))) -> c21(A__FIRST(mark(x0), recip(mark(z0))), MARK(x0)) MARK(first(x0, s(z0))) -> c21(A__FIRST(mark(x0), s(mark(z0))), MARK(x0)) MARK(first(x0, 0)) -> c21(A__FIRST(mark(x0), 0), MARK(x0)) MARK(first(x0, nil)) -> c21(A__FIRST(mark(x0), nil), MARK(x0)) MARK(first(terms(z0), x1)) -> c21(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c21(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c21(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c21(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c21(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(cons(z0, z1), x1)) -> c21(A__FIRST(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c21(A__FIRST(recip(mark(z0)), mark(x1)), MARK(recip(z0))) MARK(first(s(z0), x1)) -> c21(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, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c22_2, c23_1, c24_1, c25_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, c16_2, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2 ---------------------------------------- (85) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 6 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) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(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)) MARK(first(z0, z1)) -> c22(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(s(z0)) -> c(A__SQR(s(mark(z0))), 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(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c18(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c18(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c18(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c18(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c18(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c18(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c18(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c18(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c18(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c18(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(s(z0), x1)) -> c18(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c18(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c18(MARK(recip(z0))) MARK(add(0, x1)) -> c18(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c19(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c19(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c19(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c19(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c19(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c19(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c19(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c19(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c19(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c19(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c19(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c19(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c19(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c19(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c19(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c19(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c19(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c19(MARK(x1)) MARK(add(recip(z0), x1)) -> c19(MARK(x1)) MARK(add(nil, x1)) -> c19(MARK(x1)) MARK(dbl(terms(z0))) -> c20(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c20(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c20(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c20(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c20(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(s(z0))) -> c20(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c20(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c20(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c21(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c21(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c21(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c21(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c21(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c21(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c21(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c21(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c21(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c21(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c21(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(s(z0), x1)) -> c21(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c21(MARK(x0)) MARK(first(x0, s(z0))) -> c21(MARK(x0)) MARK(first(x0, 0)) -> c21(MARK(x0)) MARK(first(x0, nil)) -> c21(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c21(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c21(MARK(recip(z0))) S tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) MARK(first(z0, z1)) -> c22(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(s(z0)) -> c(A__SQR(s(mark(z0))), 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(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c18(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c18(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c18(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c18(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c18(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c18(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c18(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c18(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c18(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c18(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(s(z0), x1)) -> c18(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c18(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c18(MARK(recip(z0))) MARK(add(0, x1)) -> c18(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c19(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c19(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c19(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c19(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c19(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c19(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c19(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c19(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c19(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c19(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c19(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c19(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c19(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c19(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c19(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c19(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c19(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c19(MARK(x1)) MARK(add(recip(z0), x1)) -> c19(MARK(x1)) MARK(add(nil, x1)) -> c19(MARK(x1)) MARK(dbl(terms(z0))) -> c20(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c20(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c20(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c20(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c20(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(s(z0))) -> c20(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c20(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c20(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c21(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c21(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c21(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c21(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c21(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c21(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c21(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c21(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c21(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c21(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c21(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(s(z0), x1)) -> c21(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c21(MARK(x0)) MARK(first(x0, s(z0))) -> c21(MARK(x0)) MARK(first(x0, 0)) -> c21(MARK(x0)) MARK(first(x0, nil)) -> c21(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c21(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c21(MARK(recip(z0))) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c22_2, c23_1, c24_1, c25_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, c16_2, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1 ---------------------------------------- (87) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(first(z0, z1)) -> c22(A__FIRST(mark(z0), mark(z1)), MARK(z1)) by MARK(first(x0, terms(z0))) -> c22(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c22(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c22(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c22(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c22(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c22(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(x0, recip(z0))) -> c22(A__FIRST(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(first(x0, s(z0))) -> c22(A__FIRST(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(first(x0, 0)) -> c22(A__FIRST(mark(x0), 0), MARK(0)) MARK(first(x0, nil)) -> c22(A__FIRST(mark(x0), nil), MARK(nil)) MARK(first(terms(z0), x1)) -> c22(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c22(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c22(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c22(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c22(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(cons(z0, z1), x1)) -> c22(A__FIRST(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(first(recip(z0), x1)) -> c22(A__FIRST(recip(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c22(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(0, x1)) -> c22(A__FIRST(0, mark(x1)), MARK(x1)) MARK(first(nil, x1)) -> c22(A__FIRST(nil, mark(x1)), MARK(x1)) ---------------------------------------- (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) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(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)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(s(z0)) -> c(A__SQR(s(mark(z0))), 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(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c18(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c18(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c18(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c18(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c18(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c18(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c18(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c18(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c18(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c18(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(s(z0), x1)) -> c18(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c18(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c18(MARK(recip(z0))) MARK(add(0, x1)) -> c18(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c19(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c19(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c19(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c19(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c19(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c19(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c19(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c19(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c19(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c19(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c19(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c19(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c19(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c19(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c19(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c19(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c19(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c19(MARK(x1)) MARK(add(recip(z0), x1)) -> c19(MARK(x1)) MARK(add(nil, x1)) -> c19(MARK(x1)) MARK(dbl(terms(z0))) -> c20(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c20(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c20(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c20(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c20(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(s(z0))) -> c20(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c20(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c20(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c21(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c21(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c21(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c21(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c21(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c21(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c21(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c21(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c21(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c21(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c21(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(s(z0), x1)) -> c21(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c21(MARK(x0)) MARK(first(x0, s(z0))) -> c21(MARK(x0)) MARK(first(x0, 0)) -> c21(MARK(x0)) MARK(first(x0, nil)) -> c21(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c21(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c21(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c22(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c22(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c22(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c22(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c22(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c22(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(x0, recip(z0))) -> c22(A__FIRST(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(first(x0, s(z0))) -> c22(A__FIRST(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(first(x0, 0)) -> c22(A__FIRST(mark(x0), 0), MARK(0)) MARK(first(x0, nil)) -> c22(A__FIRST(mark(x0), nil), MARK(nil)) MARK(first(terms(z0), x1)) -> c22(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c22(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c22(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c22(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c22(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(cons(z0, z1), x1)) -> c22(A__FIRST(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(first(recip(z0), x1)) -> c22(A__FIRST(recip(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c22(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(0, x1)) -> c22(A__FIRST(0, mark(x1)), MARK(x1)) MARK(first(nil, x1)) -> c22(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)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(s(z0)) -> c(A__SQR(s(mark(z0))), 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(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c18(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c18(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c18(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c18(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c18(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c18(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c18(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c18(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c18(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c18(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(s(z0), x1)) -> c18(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c18(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c18(MARK(recip(z0))) MARK(add(0, x1)) -> c18(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c19(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c19(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c19(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c19(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c19(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c19(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c19(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c19(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c19(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c19(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c19(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c19(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c19(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c19(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c19(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c19(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c19(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c19(MARK(x1)) MARK(add(recip(z0), x1)) -> c19(MARK(x1)) MARK(add(nil, x1)) -> c19(MARK(x1)) MARK(dbl(terms(z0))) -> c20(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c20(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c20(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c20(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c20(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(s(z0))) -> c20(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c20(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c20(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c21(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c21(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c21(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c21(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c21(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c21(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c21(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c21(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c21(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c21(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c21(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(s(z0), x1)) -> c21(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c21(MARK(x0)) MARK(first(x0, s(z0))) -> c21(MARK(x0)) MARK(first(x0, 0)) -> c21(MARK(x0)) MARK(first(x0, nil)) -> c21(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c21(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c21(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c22(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c22(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c22(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c22(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c22(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c22(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(x0, recip(z0))) -> c22(A__FIRST(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(first(x0, s(z0))) -> c22(A__FIRST(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(first(x0, 0)) -> c22(A__FIRST(mark(x0), 0), MARK(0)) MARK(first(x0, nil)) -> c22(A__FIRST(mark(x0), nil), MARK(nil)) MARK(first(terms(z0), x1)) -> c22(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c22(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c22(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c22(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c22(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(cons(z0, z1), x1)) -> c22(A__FIRST(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(first(recip(z0), x1)) -> c22(A__FIRST(recip(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c22(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(0, x1)) -> c22(A__FIRST(0, mark(x1)), MARK(x1)) MARK(first(nil, x1)) -> c22(A__FIRST(nil, mark(x1)), MARK(x1)) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c23_1, c24_1, c25_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, c16_2, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2 ---------------------------------------- (89) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(first(x0, 0)) -> c22(A__FIRST(mark(x0), 0), MARK(0)) MARK(first(x0, nil)) -> c22(A__FIRST(mark(x0), nil), MARK(nil)) ---------------------------------------- (90) Obligation: Complexity Dependency Tuples Problem Rules: a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0) -> 0 a__sqr(s(z0)) -> s(a__add(a__sqr(mark(z0)), a__dbl(mark(z0)))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(a__dbl(mark(z0)))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(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)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(s(z0)) -> c(A__SQR(s(mark(z0))), 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(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c18(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c18(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c18(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c18(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c18(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c18(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c18(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c18(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c18(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c18(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(s(z0), x1)) -> c18(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c18(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c18(MARK(recip(z0))) MARK(add(0, x1)) -> c18(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c19(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c19(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c19(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c19(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c19(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c19(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c19(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c19(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c19(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c19(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c19(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c19(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c19(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c19(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c19(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c19(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c19(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c19(MARK(x1)) MARK(add(recip(z0), x1)) -> c19(MARK(x1)) MARK(add(nil, x1)) -> c19(MARK(x1)) MARK(dbl(terms(z0))) -> c20(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c20(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c20(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c20(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c20(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(s(z0))) -> c20(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c20(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c20(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c21(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c21(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c21(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c21(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c21(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c21(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c21(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c21(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c21(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c21(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c21(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(s(z0), x1)) -> c21(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c21(MARK(x0)) MARK(first(x0, s(z0))) -> c21(MARK(x0)) MARK(first(x0, 0)) -> c21(MARK(x0)) MARK(first(x0, nil)) -> c21(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c21(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c21(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c22(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c22(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c22(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c22(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c22(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c22(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(x0, recip(z0))) -> c22(A__FIRST(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(first(x0, s(z0))) -> c22(A__FIRST(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(first(terms(z0), x1)) -> c22(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c22(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c22(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c22(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c22(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(cons(z0, z1), x1)) -> c22(A__FIRST(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(first(recip(z0), x1)) -> c22(A__FIRST(recip(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c22(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(0, x1)) -> c22(A__FIRST(0, mark(x1)), MARK(x1)) MARK(first(nil, x1)) -> c22(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)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(s(z0)) -> c(A__SQR(s(mark(z0))), 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(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c18(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c18(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c18(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c18(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c18(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c18(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c18(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c18(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c18(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c18(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(s(z0), x1)) -> c18(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c18(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c18(MARK(recip(z0))) MARK(add(0, x1)) -> c18(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c19(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c19(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c19(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c19(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c19(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c19(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c19(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c19(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c19(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c19(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c19(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c19(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c19(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c19(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c19(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c19(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c19(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c19(MARK(x1)) MARK(add(recip(z0), x1)) -> c19(MARK(x1)) MARK(add(nil, x1)) -> c19(MARK(x1)) MARK(dbl(terms(z0))) -> c20(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c20(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c20(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c20(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c20(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(s(z0))) -> c20(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c20(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c20(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c21(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c21(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c21(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c21(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c21(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c21(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c21(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c21(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c21(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c21(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c21(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(s(z0), x1)) -> c21(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c21(MARK(x0)) MARK(first(x0, s(z0))) -> c21(MARK(x0)) MARK(first(x0, 0)) -> c21(MARK(x0)) MARK(first(x0, nil)) -> c21(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c21(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c21(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c22(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c22(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c22(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c22(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c22(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c22(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(x0, recip(z0))) -> c22(A__FIRST(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(first(x0, s(z0))) -> c22(A__FIRST(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(first(terms(z0), x1)) -> c22(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c22(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c22(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c22(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c22(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(cons(z0, z1), x1)) -> c22(A__FIRST(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(first(recip(z0), x1)) -> c22(A__FIRST(recip(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c22(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(0, x1)) -> c22(A__FIRST(0, mark(x1)), MARK(x1)) MARK(first(nil, x1)) -> c22(A__FIRST(nil, mark(x1)), MARK(x1)) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c23_1, c24_1, c25_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, c16_2, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_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) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(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)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(s(z0)) -> c(A__SQR(s(mark(z0))), 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(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c18(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c18(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c18(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c18(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c18(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c18(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c18(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c18(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c18(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c18(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(s(z0), x1)) -> c18(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c18(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c18(MARK(recip(z0))) MARK(add(0, x1)) -> c18(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c19(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c19(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c19(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c19(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c19(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c19(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c19(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c19(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c19(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c19(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c19(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c19(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c19(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c19(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c19(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c19(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c19(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c19(MARK(x1)) MARK(add(recip(z0), x1)) -> c19(MARK(x1)) MARK(add(nil, x1)) -> c19(MARK(x1)) MARK(dbl(terms(z0))) -> c20(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c20(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c20(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c20(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c20(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(s(z0))) -> c20(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c20(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c20(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c21(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c21(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c21(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c21(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c21(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c21(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c21(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c21(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c21(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c21(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c21(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(s(z0), x1)) -> c21(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c21(MARK(x0)) MARK(first(x0, s(z0))) -> c21(MARK(x0)) MARK(first(x0, 0)) -> c21(MARK(x0)) MARK(first(x0, nil)) -> c21(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c21(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c21(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c22(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c22(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c22(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c22(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c22(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c22(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c22(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c22(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c22(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c22(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c22(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c22(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c22(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c22(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c22(MARK(x1)) MARK(first(recip(z0), x1)) -> c22(MARK(x1)) MARK(first(0, x1)) -> c22(MARK(x1)) MARK(first(nil, x1)) -> c22(MARK(x1)) S tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(s(z0)) -> c(A__SQR(s(mark(z0))), 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(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c18(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c18(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c18(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c18(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c18(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c18(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c18(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c18(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c18(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c18(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(s(z0), x1)) -> c18(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c18(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c18(MARK(recip(z0))) MARK(add(0, x1)) -> c18(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c19(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c19(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c19(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c19(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c19(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c19(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c19(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c19(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c19(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c19(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c19(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c19(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c19(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c19(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c19(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c19(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c19(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c19(MARK(x1)) MARK(add(recip(z0), x1)) -> c19(MARK(x1)) MARK(add(nil, x1)) -> c19(MARK(x1)) MARK(dbl(terms(z0))) -> c20(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c20(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c20(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c20(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c20(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(s(z0))) -> c20(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c20(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c20(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c21(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c21(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c21(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c21(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c21(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c21(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c21(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c21(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c21(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c21(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c21(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(s(z0), x1)) -> c21(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c21(MARK(x0)) MARK(first(x0, s(z0))) -> c21(MARK(x0)) MARK(first(x0, 0)) -> c21(MARK(x0)) MARK(first(x0, nil)) -> c21(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c21(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c21(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c22(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c22(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c22(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c22(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c22(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c22(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c22(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c22(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c22(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c22(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c22(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c22(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c22(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c22(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c22(MARK(x1)) MARK(first(recip(z0), x1)) -> c22(MARK(x1)) MARK(first(0, x1)) -> c22(MARK(x1)) MARK(first(nil, x1)) -> c22(MARK(x1)) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c23_1, c24_1, c25_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, c16_2, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1 ---------------------------------------- (93) 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(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))) ---------------------------------------- (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) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(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)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(s(z0)) -> c(A__SQR(s(mark(z0))), 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(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c18(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c18(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c18(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c18(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c18(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c18(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c18(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c18(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c18(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c18(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(s(z0), x1)) -> c18(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c18(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c18(MARK(recip(z0))) MARK(add(0, x1)) -> c18(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c19(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c19(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c19(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c19(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c19(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c19(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c19(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c19(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c19(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c19(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c19(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c19(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c19(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c19(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c19(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c19(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c19(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c19(MARK(x1)) MARK(add(recip(z0), x1)) -> c19(MARK(x1)) MARK(add(nil, x1)) -> c19(MARK(x1)) MARK(dbl(terms(z0))) -> c20(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c20(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c20(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c20(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c20(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(s(z0))) -> c20(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c20(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c20(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c21(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c21(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c21(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c21(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c21(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c21(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c21(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c21(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c21(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c21(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c21(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(s(z0), x1)) -> c21(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c21(MARK(x0)) MARK(first(x0, s(z0))) -> c21(MARK(x0)) MARK(first(x0, 0)) -> c21(MARK(x0)) MARK(first(x0, nil)) -> c21(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c21(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c21(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c22(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c22(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c22(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c22(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c22(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c22(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c22(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c22(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c22(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c22(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c22(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c22(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c22(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c22(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c22(MARK(x1)) MARK(first(recip(z0), x1)) -> c22(MARK(x1)) MARK(first(0, x1)) -> c22(MARK(x1)) MARK(first(nil, x1)) -> c22(MARK(x1)) 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(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)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(s(z0)) -> c(A__SQR(s(mark(z0))), 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(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c18(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c18(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c18(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c18(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c18(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c18(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c18(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c18(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c18(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c18(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(s(z0), x1)) -> c18(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c18(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c18(MARK(recip(z0))) MARK(add(0, x1)) -> c18(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c19(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c19(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c19(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c19(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c19(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c19(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c19(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c19(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c19(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c19(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c19(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c19(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c19(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c19(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c19(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c19(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c19(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c19(MARK(x1)) MARK(add(recip(z0), x1)) -> c19(MARK(x1)) MARK(add(nil, x1)) -> c19(MARK(x1)) MARK(dbl(terms(z0))) -> c20(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c20(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c20(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c20(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c20(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(s(z0))) -> c20(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c20(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c20(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c21(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c21(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c21(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c21(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c21(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c21(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c21(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c21(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c21(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c21(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c21(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(s(z0), x1)) -> c21(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c21(MARK(x0)) MARK(first(x0, s(z0))) -> c21(MARK(x0)) MARK(first(x0, 0)) -> c21(MARK(x0)) MARK(first(x0, nil)) -> c21(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c21(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c21(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c22(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c22(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c22(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c22(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c22(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c22(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c22(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c22(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c22(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c22(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c22(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c22(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c22(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c22(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c22(MARK(x1)) MARK(first(recip(z0), x1)) -> c22(MARK(x1)) MARK(first(0, x1)) -> c22(MARK(x1)) MARK(first(nil, x1)) -> c22(MARK(x1)) 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(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, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c23_1, c24_1, c25_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, c16_2, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1 ---------------------------------------- (95) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (96) Obligation: Complexity Dependency Tuples Problem Rules: a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0) -> 0 a__sqr(s(z0)) -> s(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) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(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)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(s(z0)) -> c(A__SQR(s(mark(z0))), 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(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c18(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c18(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c18(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c18(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c18(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c18(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c18(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c18(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c18(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c18(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(s(z0), x1)) -> c18(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c18(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c18(MARK(recip(z0))) MARK(add(0, x1)) -> c18(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c19(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c19(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c19(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c19(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c19(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c19(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c19(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c19(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c19(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c19(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c19(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c19(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c19(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c19(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c19(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c19(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c19(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c19(MARK(x1)) MARK(add(recip(z0), x1)) -> c19(MARK(x1)) MARK(add(nil, x1)) -> c19(MARK(x1)) MARK(dbl(terms(z0))) -> c20(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c20(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c20(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c20(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c20(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(s(z0))) -> c20(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c20(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c20(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c21(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c21(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c21(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c21(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c21(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c21(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c21(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c21(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c21(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c21(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c21(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(s(z0), x1)) -> c21(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c21(MARK(x0)) MARK(first(x0, s(z0))) -> c21(MARK(x0)) MARK(first(x0, 0)) -> c21(MARK(x0)) MARK(first(x0, nil)) -> c21(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c21(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c21(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c22(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c22(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c22(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c22(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c22(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c22(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c22(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c22(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c22(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c22(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c22(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c22(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c22(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c22(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c22(MARK(x1)) MARK(first(recip(z0), x1)) -> c22(MARK(x1)) MARK(first(0, x1)) -> c22(MARK(x1)) MARK(first(nil, x1)) -> c22(MARK(x1)) 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(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)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(s(z0)) -> c(A__SQR(s(mark(z0))), 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(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c18(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c18(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c18(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c18(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c18(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c18(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c18(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c18(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c18(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c18(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(s(z0), x1)) -> c18(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c18(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c18(MARK(recip(z0))) MARK(add(0, x1)) -> c18(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c19(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c19(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c19(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c19(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c19(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c19(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c19(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c19(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c19(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c19(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c19(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c19(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c19(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c19(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c19(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c19(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c19(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c19(MARK(x1)) MARK(add(recip(z0), x1)) -> c19(MARK(x1)) MARK(add(nil, x1)) -> c19(MARK(x1)) MARK(dbl(terms(z0))) -> c20(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c20(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c20(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c20(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c20(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(s(z0))) -> c20(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c20(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c20(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c21(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c21(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c21(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c21(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c21(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c21(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c21(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c21(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c21(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c21(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c21(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(s(z0), x1)) -> c21(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c21(MARK(x0)) MARK(first(x0, s(z0))) -> c21(MARK(x0)) MARK(first(x0, 0)) -> c21(MARK(x0)) MARK(first(x0, nil)) -> c21(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c21(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c21(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c22(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c22(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c22(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c22(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c22(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c22(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c22(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c22(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c22(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c22(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c22(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c22(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c22(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c22(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c22(MARK(x1)) MARK(first(recip(z0), x1)) -> c22(MARK(x1)) MARK(first(0, x1)) -> c22(MARK(x1)) MARK(first(nil, x1)) -> c22(MARK(x1)) 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(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, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c23_1, c24_1, c25_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, c16_2, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1 ---------------------------------------- (97) 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(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))) ---------------------------------------- (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) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(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)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(s(z0)) -> c(A__SQR(s(mark(z0))), 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(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c18(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c18(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c18(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c18(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c18(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c18(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c18(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c18(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c18(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c18(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(s(z0), x1)) -> c18(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c18(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c18(MARK(recip(z0))) MARK(add(0, x1)) -> c18(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c19(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c19(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c19(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c19(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c19(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c19(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c19(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c19(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c19(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c19(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c19(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c19(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c19(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c19(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c19(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c19(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c19(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c19(MARK(x1)) MARK(add(recip(z0), x1)) -> c19(MARK(x1)) MARK(add(nil, x1)) -> c19(MARK(x1)) MARK(dbl(terms(z0))) -> c20(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c20(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c20(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c20(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c20(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(s(z0))) -> c20(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c20(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c20(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c21(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c21(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c21(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c21(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c21(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c21(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c21(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c21(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c21(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c21(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c21(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(s(z0), x1)) -> c21(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c21(MARK(x0)) MARK(first(x0, s(z0))) -> c21(MARK(x0)) MARK(first(x0, 0)) -> c21(MARK(x0)) MARK(first(x0, nil)) -> c21(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c21(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c21(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c22(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c22(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c22(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c22(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c22(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c22(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c22(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c22(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c22(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c22(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c22(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c22(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c22(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c22(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c22(MARK(x1)) MARK(first(recip(z0), x1)) -> c22(MARK(x1)) MARK(first(0, x1)) -> c22(MARK(x1)) MARK(first(nil, x1)) -> c22(MARK(x1)) 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(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(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)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(s(z0)) -> c(A__SQR(s(mark(z0))), 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(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c18(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c18(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c18(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c18(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c18(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c18(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c18(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c18(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c18(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c18(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(s(z0), x1)) -> c18(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c18(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c18(MARK(recip(z0))) MARK(add(0, x1)) -> c18(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c19(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c19(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c19(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c19(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c19(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c19(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c19(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c19(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c19(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c19(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c19(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c19(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c19(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c19(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c19(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c19(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c19(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c19(MARK(x1)) MARK(add(recip(z0), x1)) -> c19(MARK(x1)) MARK(add(nil, x1)) -> c19(MARK(x1)) MARK(dbl(terms(z0))) -> c20(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c20(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c20(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c20(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c20(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(s(z0))) -> c20(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c20(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c20(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c21(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c21(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c21(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c21(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c21(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c21(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c21(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c21(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c21(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c21(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c21(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(s(z0), x1)) -> c21(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c21(MARK(x0)) MARK(first(x0, s(z0))) -> c21(MARK(x0)) MARK(first(x0, 0)) -> c21(MARK(x0)) MARK(first(x0, nil)) -> c21(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c21(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c21(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c22(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c22(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c22(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c22(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c22(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c22(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c22(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c22(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c22(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c22(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c22(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c22(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c22(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c22(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c22(MARK(x1)) MARK(first(recip(z0), x1)) -> c22(MARK(x1)) MARK(first(0, x1)) -> c22(MARK(x1)) MARK(first(nil, x1)) -> c22(MARK(x1)) 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(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(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, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c23_1, c24_1, c25_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, c16_2, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1 ---------------------------------------- (99) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (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) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(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)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(s(z0)) -> c(A__SQR(s(mark(z0))), 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(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c18(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c18(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c18(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c18(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c18(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c18(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c18(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c18(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c18(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c18(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(s(z0), x1)) -> c18(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c18(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c18(MARK(recip(z0))) MARK(add(0, x1)) -> c18(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c19(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c19(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c19(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c19(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c19(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c19(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c19(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c19(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c19(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c19(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c19(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c19(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c19(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c19(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c19(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c19(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c19(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c19(MARK(x1)) MARK(add(recip(z0), x1)) -> c19(MARK(x1)) MARK(add(nil, x1)) -> c19(MARK(x1)) MARK(dbl(terms(z0))) -> c20(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c20(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c20(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c20(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c20(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(s(z0))) -> c20(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c20(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c20(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c21(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c21(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c21(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c21(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c21(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c21(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c21(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c21(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c21(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c21(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c21(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(s(z0), x1)) -> c21(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c21(MARK(x0)) MARK(first(x0, s(z0))) -> c21(MARK(x0)) MARK(first(x0, 0)) -> c21(MARK(x0)) MARK(first(x0, nil)) -> c21(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c21(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c21(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c22(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c22(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c22(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c22(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c22(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c22(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c22(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c22(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c22(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c22(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c22(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c22(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c22(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c22(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c22(MARK(x1)) MARK(first(recip(z0), x1)) -> c22(MARK(x1)) MARK(first(0, x1)) -> c22(MARK(x1)) MARK(first(nil, x1)) -> c22(MARK(x1)) 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(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(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)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(s(z0)) -> c(A__SQR(s(mark(z0))), 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(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c18(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c18(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c18(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c18(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c18(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c18(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c18(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c18(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c18(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c18(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(s(z0), x1)) -> c18(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c18(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c18(MARK(recip(z0))) MARK(add(0, x1)) -> c18(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c19(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c19(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c19(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c19(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c19(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c19(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c19(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c19(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c19(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c19(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c19(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c19(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c19(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c19(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c19(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c19(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c19(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c19(MARK(x1)) MARK(add(recip(z0), x1)) -> c19(MARK(x1)) MARK(add(nil, x1)) -> c19(MARK(x1)) MARK(dbl(terms(z0))) -> c20(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c20(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c20(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c20(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c20(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(s(z0))) -> c20(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c20(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c20(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c21(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c21(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c21(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c21(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c21(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c21(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c21(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c21(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c21(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c21(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c21(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(s(z0), x1)) -> c21(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c21(MARK(x0)) MARK(first(x0, s(z0))) -> c21(MARK(x0)) MARK(first(x0, 0)) -> c21(MARK(x0)) MARK(first(x0, nil)) -> c21(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c21(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c21(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c22(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c22(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c22(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c22(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c22(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c22(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c22(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c22(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c22(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c22(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c22(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c22(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c22(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c22(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c22(MARK(x1)) MARK(first(recip(z0), x1)) -> c22(MARK(x1)) MARK(first(0, x1)) -> c22(MARK(x1)) MARK(first(nil, x1)) -> c22(MARK(x1)) 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(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(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, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c23_1, c24_1, c25_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, c16_2, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1 ---------------------------------------- (101) 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, 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(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))) ---------------------------------------- (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) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(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)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(s(z0)) -> c(A__SQR(s(mark(z0))), 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(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c18(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c18(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c18(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c18(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c18(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c18(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c18(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c18(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c18(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c18(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(s(z0), x1)) -> c18(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c18(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c18(MARK(recip(z0))) MARK(add(0, x1)) -> c18(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c19(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c19(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c19(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c19(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c19(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c19(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c19(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c19(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c19(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c19(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c19(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c19(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c19(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c19(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c19(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c19(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c19(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c19(MARK(x1)) MARK(add(recip(z0), x1)) -> c19(MARK(x1)) MARK(add(nil, x1)) -> c19(MARK(x1)) MARK(dbl(terms(z0))) -> c20(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c20(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c20(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c20(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c20(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(s(z0))) -> c20(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c20(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c20(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c21(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c21(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c21(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c21(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c21(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c21(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c21(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c21(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c21(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c21(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c21(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(s(z0), x1)) -> c21(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c21(MARK(x0)) MARK(first(x0, s(z0))) -> c21(MARK(x0)) MARK(first(x0, 0)) -> c21(MARK(x0)) MARK(first(x0, nil)) -> c21(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c21(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c21(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c22(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c22(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c22(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c22(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c22(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c22(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c22(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c22(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c22(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c22(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c22(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c22(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c22(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c22(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c22(MARK(x1)) MARK(first(recip(z0), x1)) -> c22(MARK(x1)) MARK(first(0, x1)) -> c22(MARK(x1)) MARK(first(nil, x1)) -> c22(MARK(x1)) 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(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(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, 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(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)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(s(z0)) -> c(A__SQR(s(mark(z0))), 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(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c18(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c18(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c18(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c18(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c18(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c18(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c18(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c18(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c18(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c18(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(s(z0), x1)) -> c18(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c18(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c18(MARK(recip(z0))) MARK(add(0, x1)) -> c18(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c19(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c19(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c19(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c19(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c19(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c19(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c19(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c19(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c19(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c19(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c19(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c19(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c19(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c19(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c19(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c19(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c19(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c19(MARK(x1)) MARK(add(recip(z0), x1)) -> c19(MARK(x1)) MARK(add(nil, x1)) -> c19(MARK(x1)) MARK(dbl(terms(z0))) -> c20(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c20(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c20(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c20(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c20(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(s(z0))) -> c20(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c20(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c20(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c21(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c21(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c21(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c21(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c21(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c21(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c21(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c21(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c21(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c21(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c21(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(s(z0), x1)) -> c21(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c21(MARK(x0)) MARK(first(x0, s(z0))) -> c21(MARK(x0)) MARK(first(x0, 0)) -> c21(MARK(x0)) MARK(first(x0, nil)) -> c21(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c21(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c21(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c22(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c22(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c22(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c22(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c22(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c22(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c22(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c22(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c22(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c22(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c22(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c22(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c22(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c22(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c22(MARK(x1)) MARK(first(recip(z0), x1)) -> c22(MARK(x1)) MARK(first(0, x1)) -> c22(MARK(x1)) MARK(first(nil, x1)) -> c22(MARK(x1)) 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(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(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, 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(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, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c23_1, c24_1, c25_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, c16_2, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1 ---------------------------------------- (103) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 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) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(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)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(s(z0)) -> c(A__SQR(s(mark(z0))), 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(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c18(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c18(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c18(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c18(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c18(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c18(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c18(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c18(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c18(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c18(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(s(z0), x1)) -> c18(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c18(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c18(MARK(recip(z0))) MARK(add(0, x1)) -> c18(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c19(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c19(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c19(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c19(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c19(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c19(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c19(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c19(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c19(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c19(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c19(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c19(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c19(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c19(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c19(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c19(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c19(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c19(MARK(x1)) MARK(add(recip(z0), x1)) -> c19(MARK(x1)) MARK(add(nil, x1)) -> c19(MARK(x1)) MARK(dbl(terms(z0))) -> c20(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c20(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c20(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c20(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c20(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(s(z0))) -> c20(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c20(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c20(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c21(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c21(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c21(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c21(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c21(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c21(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c21(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c21(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c21(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c21(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c21(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(s(z0), x1)) -> c21(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c21(MARK(x0)) MARK(first(x0, s(z0))) -> c21(MARK(x0)) MARK(first(x0, 0)) -> c21(MARK(x0)) MARK(first(x0, nil)) -> c21(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c21(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c21(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c22(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c22(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c22(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c22(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c22(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c22(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c22(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c22(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c22(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c22(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c22(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c22(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c22(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c22(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c22(MARK(x1)) MARK(first(recip(z0), x1)) -> c22(MARK(x1)) MARK(first(0, x1)) -> c22(MARK(x1)) MARK(first(nil, x1)) -> c22(MARK(x1)) 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(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(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, 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(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)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(s(z0)) -> c(A__SQR(s(mark(z0))), 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(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c18(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c18(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c18(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c18(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c18(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c18(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c18(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c18(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c18(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c18(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(s(z0), x1)) -> c18(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c18(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c18(MARK(recip(z0))) MARK(add(0, x1)) -> c18(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c19(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c19(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c19(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c19(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c19(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c19(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c19(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c19(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c19(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c19(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c19(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c19(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c19(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c19(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c19(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c19(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c19(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c19(MARK(x1)) MARK(add(recip(z0), x1)) -> c19(MARK(x1)) MARK(add(nil, x1)) -> c19(MARK(x1)) MARK(dbl(terms(z0))) -> c20(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c20(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c20(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c20(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c20(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(s(z0))) -> c20(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c20(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c20(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c21(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c21(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c21(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c21(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c21(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c21(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c21(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c21(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c21(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c21(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c21(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(s(z0), x1)) -> c21(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c21(MARK(x0)) MARK(first(x0, s(z0))) -> c21(MARK(x0)) MARK(first(x0, 0)) -> c21(MARK(x0)) MARK(first(x0, nil)) -> c21(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c21(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c21(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c22(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c22(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c22(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c22(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c22(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c22(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c22(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c22(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c22(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c22(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c22(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c22(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c22(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c22(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c22(MARK(x1)) MARK(first(recip(z0), x1)) -> c22(MARK(x1)) MARK(first(0, x1)) -> c22(MARK(x1)) MARK(first(nil, x1)) -> c22(MARK(x1)) 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(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(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, 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(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, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c23_1, c24_1, c25_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, c16_2, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1 ---------------------------------------- (105) 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(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))) ---------------------------------------- (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) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(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)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(MARK(z0)) A__TERMS(first(z0, z1)) -> c(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), 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(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> 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c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c18(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c18(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c18(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c18(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c18(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c18(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c18(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c18(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c18(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c18(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(s(z0), x1)) -> c18(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c18(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c18(MARK(recip(z0))) MARK(add(0, x1)) -> c18(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c19(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c19(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c19(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c19(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c19(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c19(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c19(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c19(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c19(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c19(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c19(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c19(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c19(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c19(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c19(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c19(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c19(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c19(MARK(x1)) MARK(add(recip(z0), x1)) -> c19(MARK(x1)) 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MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c21(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c21(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c21(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c21(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c21(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c21(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(s(z0), x1)) -> c21(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c21(MARK(x0)) MARK(first(x0, s(z0))) -> c21(MARK(x0)) MARK(first(x0, 0)) -> c21(MARK(x0)) MARK(first(x0, nil)) -> c21(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c21(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c21(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c22(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c22(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c22(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c22(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c22(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c22(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c22(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c22(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c22(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c22(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c22(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c22(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c22(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c22(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c22(MARK(x1)) MARK(first(recip(z0), x1)) -> c22(MARK(x1)) MARK(first(0, x1)) -> c22(MARK(x1)) MARK(first(nil, x1)) -> c22(MARK(x1)) 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(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(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, 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(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(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)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(MARK(z0)) A__TERMS(first(z0, z1)) -> c(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), 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(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c18(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c18(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c18(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c18(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c18(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c18(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c18(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c18(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c18(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c18(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(s(z0), x1)) -> c18(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c18(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c18(MARK(recip(z0))) MARK(add(0, x1)) -> c18(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c19(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c19(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c19(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c19(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c19(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c19(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c19(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c19(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c19(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c19(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c19(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c19(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c19(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c19(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c19(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c19(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c19(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c19(MARK(x1)) MARK(add(recip(z0), x1)) -> c19(MARK(x1)) MARK(add(nil, x1)) -> c19(MARK(x1)) MARK(dbl(terms(z0))) -> c20(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c20(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c20(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c20(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c20(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(s(z0))) -> c20(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c20(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c20(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c21(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c21(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c21(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c21(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c21(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c21(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c21(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c21(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c21(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c21(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c21(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(s(z0), x1)) -> c21(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c21(MARK(x0)) MARK(first(x0, s(z0))) -> c21(MARK(x0)) MARK(first(x0, 0)) -> c21(MARK(x0)) MARK(first(x0, nil)) -> c21(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c21(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c21(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c22(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c22(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c22(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c22(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c22(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c22(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c22(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c22(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c22(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c22(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c22(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c22(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c22(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c22(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c22(MARK(x1)) MARK(first(recip(z0), x1)) -> c22(MARK(x1)) MARK(first(0, x1)) -> c22(MARK(x1)) MARK(first(nil, x1)) -> c22(MARK(x1)) 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(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(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, 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(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(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, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c23_1, c24_1, c25_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, c16_2, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1 ---------------------------------------- (107) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (108) Obligation: Complexity Dependency Tuples Problem Rules: a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0) -> 0 a__sqr(s(z0)) -> s(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) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(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)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(MARK(z0)) A__TERMS(first(z0, z1)) -> c(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), 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(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c18(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c18(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c18(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c18(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c18(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c18(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c18(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c18(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c18(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c18(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(s(z0), x1)) -> c18(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c18(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c18(MARK(recip(z0))) MARK(add(0, x1)) -> c18(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c19(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c19(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c19(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c19(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c19(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c19(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c19(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c19(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c19(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c19(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c19(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c19(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c19(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c19(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c19(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c19(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c19(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c19(MARK(x1)) MARK(add(recip(z0), x1)) -> c19(MARK(x1)) MARK(add(nil, x1)) -> c19(MARK(x1)) MARK(dbl(terms(z0))) -> c20(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c20(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c20(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c20(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c20(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(s(z0))) -> c20(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c20(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c20(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c21(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c21(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c21(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c21(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c21(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c21(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c21(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c21(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c21(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c21(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c21(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(s(z0), x1)) -> c21(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c21(MARK(x0)) MARK(first(x0, s(z0))) -> c21(MARK(x0)) MARK(first(x0, 0)) -> c21(MARK(x0)) MARK(first(x0, nil)) -> c21(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c21(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c21(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c22(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c22(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c22(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c22(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c22(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c22(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c22(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c22(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c22(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c22(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c22(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c22(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c22(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c22(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c22(MARK(x1)) MARK(first(recip(z0), x1)) -> c22(MARK(x1)) MARK(first(0, x1)) -> c22(MARK(x1)) MARK(first(nil, x1)) -> c22(MARK(x1)) 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(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(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, 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(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(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)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(MARK(z0)) A__TERMS(first(z0, z1)) -> c(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__TERMS(s(z0)) -> c(A__SQR(s(mark(z0))), 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(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c18(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c18(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c18(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c18(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c18(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c18(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c18(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c18(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c18(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c18(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(s(z0), x1)) -> c18(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c18(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c18(MARK(recip(z0))) MARK(add(0, x1)) -> c18(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c19(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c19(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c19(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c19(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c19(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c19(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c19(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c19(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c19(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c19(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c19(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c19(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c19(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c19(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c19(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c19(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c19(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c19(MARK(x1)) MARK(add(recip(z0), x1)) -> c19(MARK(x1)) MARK(add(nil, x1)) -> c19(MARK(x1)) MARK(dbl(terms(z0))) -> c20(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c20(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c20(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c20(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c20(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(s(z0))) -> c20(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c20(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c20(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c21(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c21(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c21(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c21(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c21(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c21(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c21(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c21(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c21(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c21(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c21(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(s(z0), x1)) -> c21(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c21(MARK(x0)) MARK(first(x0, s(z0))) -> c21(MARK(x0)) MARK(first(x0, 0)) -> c21(MARK(x0)) MARK(first(x0, nil)) -> c21(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c21(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c21(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c22(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c22(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c22(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c22(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c22(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c22(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c22(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c22(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c22(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c22(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c22(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c22(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c22(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c22(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c22(MARK(x1)) MARK(first(recip(z0), x1)) -> c22(MARK(x1)) MARK(first(0, x1)) -> c22(MARK(x1)) MARK(first(nil, x1)) -> c22(MARK(x1)) 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(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(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, 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(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(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, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c23_1, c24_1, c25_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, c16_2, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1 ---------------------------------------- (109) 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, 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(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))) ---------------------------------------- (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) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(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)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), 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MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c19(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c19(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c19(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c19(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c19(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c19(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c19(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c19(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c19(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c19(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c19(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c19(A__ADD(0, mark(x1)), MARK(x1)) 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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, 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(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(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, 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(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)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, 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z1))) -> c19(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c19(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c19(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c19(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c19(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c19(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c19(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c19(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c19(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c19(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c19(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c19(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c19(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c19(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c19(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c19(MARK(x1)) MARK(add(recip(z0), x1)) -> c19(MARK(x1)) MARK(add(nil, x1)) -> c19(MARK(x1)) MARK(dbl(terms(z0))) -> c20(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c20(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c20(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c20(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c20(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(s(z0))) -> c20(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c20(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c20(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c21(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c21(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c21(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c21(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c21(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c21(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c21(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c21(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c21(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c21(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c21(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(s(z0), x1)) -> c21(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c21(MARK(x0)) MARK(first(x0, s(z0))) -> c21(MARK(x0)) MARK(first(x0, 0)) -> c21(MARK(x0)) MARK(first(x0, nil)) -> c21(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c21(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c21(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c22(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c22(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c22(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c22(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c22(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c22(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c22(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c22(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c22(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c22(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c22(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c22(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c22(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c22(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c22(MARK(x1)) MARK(first(recip(z0), x1)) -> c22(MARK(x1)) MARK(first(0, x1)) -> c22(MARK(x1)) MARK(first(nil, x1)) -> c22(MARK(x1)) 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(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(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, 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(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(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, 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(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, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c23_1, c24_1, c25_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, c16_2, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1 ---------------------------------------- (111) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 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) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(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)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c18(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c18(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c18(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c18(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c18(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c18(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c18(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c18(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c18(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c18(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(s(z0), x1)) -> c18(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c18(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c18(MARK(recip(z0))) MARK(add(0, x1)) -> c18(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c19(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c19(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c19(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c19(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c19(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c19(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c19(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c19(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c19(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c19(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c19(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c19(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c19(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c19(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c19(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c19(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c19(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c19(MARK(x1)) MARK(add(recip(z0), x1)) -> c19(MARK(x1)) MARK(add(nil, x1)) -> c19(MARK(x1)) MARK(dbl(terms(z0))) -> c20(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c20(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c20(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c20(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c20(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(s(z0))) -> c20(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c20(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c20(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c21(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c21(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c21(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c21(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c21(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c21(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c21(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c21(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c21(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c21(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c21(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(s(z0), x1)) -> c21(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c21(MARK(x0)) MARK(first(x0, s(z0))) -> c21(MARK(x0)) MARK(first(x0, 0)) -> c21(MARK(x0)) MARK(first(x0, nil)) -> c21(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c21(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c21(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c22(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c22(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c22(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c22(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c22(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c22(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c22(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c22(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c22(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c22(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c22(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c22(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c22(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c22(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c22(MARK(x1)) MARK(first(recip(z0), x1)) -> c22(MARK(x1)) MARK(first(0, x1)) -> c22(MARK(x1)) MARK(first(nil, x1)) -> c22(MARK(x1)) 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(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(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, 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(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(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, 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(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)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c18(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c18(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c18(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c18(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c18(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c18(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c18(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c18(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c18(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c18(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(s(z0), x1)) -> c18(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c18(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c18(MARK(recip(z0))) MARK(add(0, x1)) -> c18(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c19(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c19(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c19(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c19(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c19(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c19(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c19(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c19(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c19(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c19(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c19(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c19(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c19(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c19(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c19(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c19(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c19(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c19(MARK(x1)) MARK(add(recip(z0), x1)) -> c19(MARK(x1)) MARK(add(nil, x1)) -> c19(MARK(x1)) MARK(dbl(terms(z0))) -> c20(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c20(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c20(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c20(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c20(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(s(z0))) -> c20(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c20(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c20(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c21(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c21(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c21(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c21(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c21(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c21(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c21(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c21(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c21(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c21(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c21(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(s(z0), x1)) -> c21(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c21(MARK(x0)) MARK(first(x0, s(z0))) -> c21(MARK(x0)) MARK(first(x0, 0)) -> c21(MARK(x0)) MARK(first(x0, nil)) -> c21(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c21(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c21(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c22(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c22(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c22(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c22(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c22(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c22(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c22(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c22(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c22(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c22(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c22(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c22(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c22(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c22(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c22(MARK(x1)) MARK(first(recip(z0), x1)) -> c22(MARK(x1)) MARK(first(0, x1)) -> c22(MARK(x1)) MARK(first(nil, x1)) -> c22(MARK(x1)) 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(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(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, 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(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(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, 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(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, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c23_1, c24_1, c25_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, c16_2, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1 ---------------------------------------- (113) 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(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(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)) ---------------------------------------- (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) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(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)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c18(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c18(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c18(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c18(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c18(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c18(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c18(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c18(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c18(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c18(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(s(z0), x1)) -> c18(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c18(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c18(MARK(recip(z0))) MARK(add(0, x1)) -> c18(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c19(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c19(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c19(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c19(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c19(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), 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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(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, 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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(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__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(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(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)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c18(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c18(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c18(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c18(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c18(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c18(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c18(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c18(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c18(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c18(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(s(z0), x1)) -> c18(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c18(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c18(MARK(recip(z0))) MARK(add(0, x1)) -> c18(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c19(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c19(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c19(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c19(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c19(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c19(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c19(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c19(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c19(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c19(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c19(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c19(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c19(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c19(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c19(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c19(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c19(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c19(MARK(x1)) MARK(add(recip(z0), x1)) -> c19(MARK(x1)) MARK(add(nil, x1)) -> c19(MARK(x1)) MARK(dbl(terms(z0))) -> c20(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c20(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c20(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c20(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c20(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(s(z0))) -> c20(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c20(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c20(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c21(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c21(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c21(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c21(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c21(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c21(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c21(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c21(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c21(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c21(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c21(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(s(z0), x1)) -> c21(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c21(MARK(x0)) MARK(first(x0, s(z0))) -> c21(MARK(x0)) MARK(first(x0, 0)) -> c21(MARK(x0)) MARK(first(x0, nil)) -> c21(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c21(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c21(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c22(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c22(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c22(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c22(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c22(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c22(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c22(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c22(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c22(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c22(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c22(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c22(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c22(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c22(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c22(MARK(x1)) MARK(first(recip(z0), x1)) -> c22(MARK(x1)) MARK(first(0, x1)) -> c22(MARK(x1)) MARK(first(nil, x1)) -> c22(MARK(x1)) 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(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(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, 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(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(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, 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(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__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(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(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, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c23_1, c24_1, c25_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, c16_2, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1 ---------------------------------------- (115) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 5 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) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(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)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c18(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c18(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c18(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c18(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c18(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c18(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c18(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c18(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c18(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c18(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(s(z0), x1)) -> c18(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c18(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c18(MARK(recip(z0))) MARK(add(0, x1)) -> c18(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c19(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c19(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c19(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c19(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c19(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c19(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c19(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c19(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c19(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c19(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c19(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c19(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c19(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c19(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c19(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c19(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c19(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c19(MARK(x1)) MARK(add(recip(z0), x1)) -> c19(MARK(x1)) MARK(add(nil, x1)) -> c19(MARK(x1)) MARK(dbl(terms(z0))) -> c20(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c20(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c20(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c20(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c20(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(s(z0))) -> c20(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c20(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c20(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c21(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c21(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c21(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c21(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c21(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c21(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c21(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c21(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c21(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c21(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c21(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(s(z0), x1)) -> c21(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c21(MARK(x0)) MARK(first(x0, s(z0))) -> c21(MARK(x0)) MARK(first(x0, 0)) -> c21(MARK(x0)) MARK(first(x0, nil)) -> c21(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c21(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c21(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c22(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c22(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c22(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c22(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c22(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c22(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c22(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c22(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c22(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c22(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c22(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c22(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c22(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c22(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c22(MARK(x1)) MARK(first(recip(z0), x1)) -> c22(MARK(x1)) MARK(first(0, x1)) -> c22(MARK(x1)) MARK(first(nil, x1)) -> c22(MARK(x1)) 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(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(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, 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(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(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, 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(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__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(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(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)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), 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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(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, 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(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__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(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(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, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c23_1, c24_1, c25_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, c16_2, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1 ---------------------------------------- (117) 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(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))) ---------------------------------------- (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) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(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)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c18(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c18(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c18(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c18(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c18(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c18(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c18(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c18(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c18(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c18(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(s(z0), x1)) -> c18(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c18(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c18(MARK(recip(z0))) MARK(add(0, x1)) -> c18(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c19(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c19(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c19(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c19(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c19(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c19(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c19(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c19(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c19(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c19(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c19(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c19(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c19(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c19(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c19(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c19(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c19(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c19(MARK(x1)) MARK(add(recip(z0), x1)) -> c19(MARK(x1)) MARK(add(nil, x1)) -> c19(MARK(x1)) MARK(dbl(terms(z0))) -> c20(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c20(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c20(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c20(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c20(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(s(z0))) -> c20(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c20(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c20(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c21(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c21(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c21(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c21(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c21(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c21(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c21(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c21(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c21(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c21(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c21(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(s(z0), x1)) -> c21(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c21(MARK(x0)) MARK(first(x0, s(z0))) -> c21(MARK(x0)) MARK(first(x0, 0)) -> c21(MARK(x0)) MARK(first(x0, nil)) -> c21(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c21(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c21(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c22(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c22(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c22(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c22(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c22(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c22(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c22(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c22(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c22(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c22(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c22(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c22(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c22(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c22(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c22(MARK(x1)) MARK(first(recip(z0), x1)) -> c22(MARK(x1)) MARK(first(0, x1)) -> c22(MARK(x1)) MARK(first(nil, x1)) -> c22(MARK(x1)) 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(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(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, 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(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(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, 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(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__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(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(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(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)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c18(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c18(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c18(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c18(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c18(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c18(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c18(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c18(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c18(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c18(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(s(z0), x1)) -> c18(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c18(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c18(MARK(recip(z0))) MARK(add(0, x1)) -> c18(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c19(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c19(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c19(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c19(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c19(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c19(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c19(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c19(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c19(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c19(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c19(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c19(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c19(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c19(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c19(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c19(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c19(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c19(MARK(x1)) MARK(add(recip(z0), x1)) -> c19(MARK(x1)) MARK(add(nil, x1)) -> c19(MARK(x1)) MARK(dbl(terms(z0))) -> c20(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c20(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c20(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c20(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c20(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(s(z0))) -> c20(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c20(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c20(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c21(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c21(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c21(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c21(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c21(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c21(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c21(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c21(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c21(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c21(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c21(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(s(z0), x1)) -> c21(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c21(MARK(x0)) MARK(first(x0, s(z0))) -> c21(MARK(x0)) MARK(first(x0, 0)) -> c21(MARK(x0)) MARK(first(x0, nil)) -> c21(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c21(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c21(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c22(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c22(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c22(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c22(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c22(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c22(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c22(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c22(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c22(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c22(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c22(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c22(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c22(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c22(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c22(MARK(x1)) MARK(first(recip(z0), x1)) -> c22(MARK(x1)) MARK(first(0, x1)) -> c22(MARK(x1)) MARK(first(nil, x1)) -> c22(MARK(x1)) 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(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(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, 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(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(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, 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(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__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(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(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(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, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c23_1, c24_1, c25_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, c16_2, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_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) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(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)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c18(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c18(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c18(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c18(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c18(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c18(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c18(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c18(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c18(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c18(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(s(z0), x1)) -> c18(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c18(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c18(MARK(recip(z0))) MARK(add(0, x1)) -> c18(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c19(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c19(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c19(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c19(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c19(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c19(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c19(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c19(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c19(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c19(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c19(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c19(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c19(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c19(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c19(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c19(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c19(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c19(MARK(x1)) MARK(add(recip(z0), x1)) -> c19(MARK(x1)) MARK(add(nil, x1)) -> c19(MARK(x1)) MARK(dbl(terms(z0))) -> c20(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c20(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c20(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c20(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c20(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(s(z0))) -> c20(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c20(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c20(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c21(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c21(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c21(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c21(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c21(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c21(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c21(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c21(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c21(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c21(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c21(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(s(z0), x1)) -> c21(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c21(MARK(x0)) MARK(first(x0, s(z0))) -> c21(MARK(x0)) MARK(first(x0, 0)) -> c21(MARK(x0)) MARK(first(x0, nil)) -> c21(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c21(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c21(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c22(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c22(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c22(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c22(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c22(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c22(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c22(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c22(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c22(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c22(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c22(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c22(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c22(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c22(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c22(MARK(x1)) MARK(first(recip(z0), x1)) -> c22(MARK(x1)) MARK(first(0, x1)) -> c22(MARK(x1)) MARK(first(nil, x1)) -> c22(MARK(x1)) 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(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(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, 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(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, 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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, 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(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__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(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(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(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)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c18(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c18(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c18(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c18(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c18(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c18(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c18(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c18(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c18(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c18(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(s(z0), x1)) -> c18(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c18(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c18(MARK(recip(z0))) MARK(add(0, x1)) -> c18(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c19(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c19(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c19(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c19(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c19(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c19(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c19(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c19(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c19(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c19(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c19(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c19(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c19(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c19(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c19(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c19(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c19(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c19(MARK(x1)) MARK(add(recip(z0), x1)) -> c19(MARK(x1)) MARK(add(nil, x1)) -> c19(MARK(x1)) MARK(dbl(terms(z0))) -> c20(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c20(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c20(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c20(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c20(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(s(z0))) -> c20(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c20(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c20(MARK(recip(z0))) MARK(first(x0, 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A__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(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(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, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c23_1, c24_1, c25_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, c16_2, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1 ---------------------------------------- (121) 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(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))) ---------------------------------------- (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) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(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)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c18(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c18(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c18(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c18(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c18(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c18(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c18(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c18(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c18(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c18(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(s(z0), x1)) -> c18(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c18(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c18(MARK(recip(z0))) MARK(add(0, x1)) -> c18(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c19(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c19(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c19(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c19(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c19(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c19(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c19(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c19(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c19(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c19(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c19(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c19(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c19(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c19(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c19(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c19(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c19(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c19(MARK(x1)) MARK(add(recip(z0), x1)) -> c19(MARK(x1)) MARK(add(nil, x1)) -> c19(MARK(x1)) MARK(dbl(terms(z0))) -> c20(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c20(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c20(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c20(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c20(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(s(z0))) -> c20(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c20(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c20(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c21(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c21(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c21(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c21(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c21(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c21(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c21(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c21(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c21(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c21(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c21(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(s(z0), x1)) -> c21(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c21(MARK(x0)) MARK(first(x0, s(z0))) -> c21(MARK(x0)) MARK(first(x0, 0)) -> c21(MARK(x0)) MARK(first(x0, nil)) -> c21(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c21(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c21(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c22(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c22(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c22(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c22(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c22(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c22(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c22(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c22(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c22(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c22(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c22(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c22(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c22(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c22(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c22(MARK(x1)) MARK(first(recip(z0), x1)) -> c22(MARK(x1)) MARK(first(0, x1)) -> c22(MARK(x1)) MARK(first(nil, x1)) -> c22(MARK(x1)) 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(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(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, 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(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(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, 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(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__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(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(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(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(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)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c18(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c18(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c18(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c18(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c18(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c18(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c18(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c18(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c18(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c18(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(s(z0), x1)) -> c18(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c18(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c18(MARK(recip(z0))) MARK(add(0, x1)) -> c18(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c19(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c19(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c19(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c19(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c19(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c19(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c19(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c19(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c19(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c19(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c19(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c19(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c19(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c19(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c19(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c19(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c19(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c19(MARK(x1)) MARK(add(recip(z0), x1)) -> c19(MARK(x1)) MARK(add(nil, x1)) -> c19(MARK(x1)) MARK(dbl(terms(z0))) -> c20(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c20(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c20(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c20(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c20(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(s(z0))) -> c20(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c20(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c20(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c21(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c21(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c21(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c21(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c21(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c21(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c21(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c21(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c21(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c21(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c21(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(s(z0), x1)) -> c21(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c21(MARK(x0)) MARK(first(x0, s(z0))) -> c21(MARK(x0)) MARK(first(x0, 0)) -> c21(MARK(x0)) MARK(first(x0, nil)) -> c21(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c21(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c21(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c22(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c22(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c22(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c22(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c22(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c22(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c22(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c22(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c22(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c22(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c22(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c22(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c22(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c22(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c22(MARK(x1)) MARK(first(recip(z0), x1)) -> c22(MARK(x1)) MARK(first(0, x1)) -> c22(MARK(x1)) MARK(first(nil, x1)) -> c22(MARK(x1)) 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(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(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, 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(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(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, 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(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__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(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(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(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(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, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c23_1, c24_1, c25_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, c16_2, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1 ---------------------------------------- (123) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 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) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(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)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c18(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c18(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c18(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c18(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c18(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c18(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c18(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c18(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c18(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c18(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(s(z0), x1)) -> c18(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c18(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c18(MARK(recip(z0))) MARK(add(0, x1)) -> c18(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c19(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c19(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c19(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c19(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c19(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c19(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c19(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c19(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c19(A__ADD(a__terms(mark(z0)), mark(x1)), 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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(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(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(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(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)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), 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z1))) -> c20(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(s(z0))) -> c20(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c20(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c20(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c21(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c21(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c21(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c21(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c21(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c21(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c21(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c21(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c21(A__FIRST(a__add(mark(z0), mark(z1)), 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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(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)))) 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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(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(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, 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(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__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(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(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(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(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, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c23_1, c24_1, c25_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, c16_2, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1 ---------------------------------------- (125) 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, 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(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))) ---------------------------------------- (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) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(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)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c18(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c18(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c18(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c18(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c18(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c18(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c18(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c18(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c18(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c18(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(s(z0), x1)) -> c18(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c18(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c18(MARK(recip(z0))) MARK(add(0, x1)) -> c18(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c19(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c19(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c19(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c19(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c19(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c19(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c19(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c19(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c19(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c19(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c19(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c19(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c19(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c19(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) 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A__SQR(mark(first(z0, z1))), MARK(first(z0, z1))) 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(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(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(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, 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(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)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c18(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c18(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c18(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c18(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c18(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c18(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c18(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c18(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c18(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c18(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(s(z0), x1)) -> c18(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c18(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c18(MARK(recip(z0))) MARK(add(0, x1)) -> c18(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c19(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c19(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c19(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c19(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c19(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c19(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c19(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c19(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c19(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c19(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c19(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c19(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c19(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c19(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c19(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c19(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c19(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c19(MARK(x1)) MARK(add(recip(z0), x1)) -> c19(MARK(x1)) MARK(add(nil, x1)) -> c19(MARK(x1)) MARK(dbl(terms(z0))) -> c20(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c20(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c20(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c20(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c20(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(s(z0))) -> c20(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c20(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c20(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c21(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c21(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c21(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c21(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c21(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c21(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c21(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c21(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c21(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c21(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c21(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(s(z0), x1)) -> c21(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c21(MARK(x0)) MARK(first(x0, s(z0))) -> c21(MARK(x0)) MARK(first(x0, 0)) -> c21(MARK(x0)) MARK(first(x0, nil)) -> c21(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c21(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c21(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c22(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c22(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c22(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c22(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c22(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c22(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c22(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c22(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c22(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c22(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c22(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c22(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c22(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c22(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c22(MARK(x1)) MARK(first(recip(z0), x1)) -> c22(MARK(x1)) MARK(first(0, x1)) -> c22(MARK(x1)) MARK(first(nil, x1)) -> c22(MARK(x1)) 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(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(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, 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(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(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, 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(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__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(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(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(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(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, 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(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, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c23_1, c24_1, c25_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, c16_2, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1 ---------------------------------------- (127) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 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) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(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)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c18(A__ADD(mark(x0), cons(mark(z0), 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a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c19(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c19(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c19(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c19(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c19(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c19(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c19(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c19(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c19(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c19(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c19(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c19(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c19(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c19(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c19(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c19(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c19(MARK(x1)) MARK(add(recip(z0), x1)) -> c19(MARK(x1)) MARK(add(nil, x1)) -> c19(MARK(x1)) MARK(dbl(terms(z0))) -> c20(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c20(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c20(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c20(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c20(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(s(z0))) -> c20(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c20(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c20(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c21(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c21(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c21(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c21(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c21(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c21(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c21(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c21(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c21(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c21(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c21(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(s(z0), x1)) -> c21(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c21(MARK(x0)) MARK(first(x0, s(z0))) -> c21(MARK(x0)) MARK(first(x0, 0)) -> c21(MARK(x0)) MARK(first(x0, nil)) -> c21(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c21(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c21(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c22(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c22(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c22(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c22(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c22(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c22(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c22(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c22(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c22(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c22(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c22(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c22(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c22(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c22(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c22(MARK(x1)) MARK(first(recip(z0), x1)) -> c22(MARK(x1)) MARK(first(0, x1)) -> c22(MARK(x1)) MARK(first(nil, x1)) -> c22(MARK(x1)) 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(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), 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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(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(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, 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(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__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(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(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(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(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, 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(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)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c18(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c18(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c18(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c18(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c18(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c18(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c18(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c18(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c18(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c18(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(s(z0), x1)) -> c18(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c18(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c18(MARK(recip(z0))) MARK(add(0, x1)) -> c18(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c19(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c19(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c19(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c19(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c19(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c19(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c19(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c19(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c19(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c19(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c19(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c19(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c19(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c19(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c19(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c19(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c19(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c19(MARK(x1)) MARK(add(recip(z0), x1)) -> c19(MARK(x1)) MARK(add(nil, x1)) -> c19(MARK(x1)) MARK(dbl(terms(z0))) -> c20(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c20(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c20(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c20(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c20(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(s(z0))) -> c20(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c20(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c20(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c21(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c21(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c21(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c21(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) 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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(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(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, 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(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, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c23_1, c24_1, c25_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, c16_2, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1 ---------------------------------------- (129) 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(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))) ---------------------------------------- (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) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(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)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c18(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c18(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c18(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c18(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c18(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c18(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c18(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c18(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c18(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c18(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(s(z0), x1)) -> c18(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c18(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c18(MARK(recip(z0))) MARK(add(0, x1)) -> c18(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c19(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c19(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c19(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c19(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c19(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c19(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c19(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c19(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c19(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c19(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c19(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c19(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c19(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c19(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c19(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c19(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c19(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c19(MARK(x1)) MARK(add(recip(z0), x1)) -> c19(MARK(x1)) MARK(add(nil, x1)) -> c19(MARK(x1)) MARK(dbl(terms(z0))) -> c20(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c20(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c20(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c20(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c20(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(s(z0))) -> c20(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c20(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c20(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c21(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c21(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c21(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c21(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c21(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c21(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c21(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c21(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c21(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c21(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c21(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(s(z0), x1)) -> c21(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c21(MARK(x0)) MARK(first(x0, s(z0))) -> c21(MARK(x0)) MARK(first(x0, 0)) -> c21(MARK(x0)) MARK(first(x0, nil)) -> c21(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c21(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c21(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c22(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c22(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c22(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c22(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c22(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c22(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c22(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c22(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c22(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c22(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c22(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c22(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c22(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c22(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c22(MARK(x1)) MARK(first(recip(z0), x1)) -> c22(MARK(x1)) MARK(first(0, x1)) -> c22(MARK(x1)) MARK(first(nil, x1)) -> c22(MARK(x1)) 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(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(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, 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(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(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, 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(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__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(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(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(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(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, 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(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(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)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), 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MARK(recip(z0))) MARK(add(x0, s(z0))) -> c19(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c19(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c19(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c19(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c19(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c19(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c19(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c19(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c19(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c19(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c19(MARK(x1)) MARK(add(recip(z0), x1)) -> c19(MARK(x1)) MARK(add(nil, x1)) -> c19(MARK(x1)) MARK(dbl(terms(z0))) -> c20(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c20(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) 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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(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, 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(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(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, 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(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__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(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(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(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(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, 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(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(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, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c23_1, c24_1, c25_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, c16_2, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1 ---------------------------------------- (131) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (132) Obligation: Complexity Dependency Tuples Problem Rules: a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0) -> 0 a__sqr(s(z0)) -> s(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) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(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)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), 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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(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(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, 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(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__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(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(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(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(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, 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(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(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)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c18(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c18(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c18(A__ADD(mark(x0), 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MARK(first(dbl(z0), x1)) -> c22(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c22(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c22(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c22(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c22(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c22(MARK(x1)) MARK(first(recip(z0), x1)) -> c22(MARK(x1)) MARK(first(0, x1)) -> c22(MARK(x1)) MARK(first(nil, x1)) -> c22(MARK(x1)) 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(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(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, 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(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(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, 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(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__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(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(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(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(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, 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(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(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, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c23_1, c24_1, c25_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, c16_2, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1 ---------------------------------------- (133) 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, 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(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))) ---------------------------------------- (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) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(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)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), 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MARK(first(terms(z0), x1)) -> c22(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c22(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c22(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c22(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c22(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c22(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c22(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c22(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c22(MARK(x1)) MARK(first(recip(z0), x1)) -> c22(MARK(x1)) MARK(first(0, x1)) -> c22(MARK(x1)) MARK(first(nil, x1)) -> c22(MARK(x1)) 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))) -> 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c(A__SQR(a__add(mark(x0), a__first(mark(z0), mark(z1)))), MARK(add(x0, first(z0, z1)))) 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(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(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, 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(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__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(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(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(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(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, 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(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(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, 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(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)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> 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c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c18(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c18(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c18(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c18(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c18(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c18(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c18(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c18(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c18(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c18(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(s(z0), x1)) -> c18(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c18(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c18(MARK(recip(z0))) MARK(add(0, x1)) -> c18(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c19(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c19(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c19(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c19(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c19(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c19(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c19(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c19(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c19(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c19(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c19(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c19(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c19(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c19(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c19(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c19(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c19(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c19(MARK(x1)) MARK(add(recip(z0), x1)) -> c19(MARK(x1)) 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MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c21(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c21(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c21(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c21(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c21(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c21(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(s(z0), x1)) -> c21(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c21(MARK(x0)) MARK(first(x0, s(z0))) -> c21(MARK(x0)) MARK(first(x0, 0)) -> c21(MARK(x0)) MARK(first(x0, nil)) -> c21(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c21(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c21(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c22(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c22(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c22(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c22(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c22(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c22(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c22(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c22(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c22(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c22(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c22(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c22(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c22(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c22(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c22(MARK(x1)) MARK(first(recip(z0), x1)) -> c22(MARK(x1)) MARK(first(0, x1)) -> c22(MARK(x1)) MARK(first(nil, x1)) -> c22(MARK(x1)) 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(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(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, 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(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(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, 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(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__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(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(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(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(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, 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(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(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, 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(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, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c23_1, c24_1, c25_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, c16_2, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1 ---------------------------------------- (135) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 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) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(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)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c18(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c18(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c18(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c18(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c18(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c18(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c18(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c18(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c18(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c18(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(s(z0), x1)) -> c18(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c18(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c18(MARK(recip(z0))) MARK(add(0, x1)) -> c18(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c19(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c19(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c19(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c19(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c19(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c19(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c19(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c19(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c19(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c19(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c19(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c19(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c19(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c19(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c19(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c19(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c19(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c19(MARK(x1)) MARK(add(recip(z0), x1)) -> c19(MARK(x1)) MARK(add(nil, x1)) -> c19(MARK(x1)) MARK(dbl(terms(z0))) -> c20(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c20(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c20(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c20(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c20(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(s(z0))) -> c20(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c20(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c20(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c21(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c21(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c21(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c21(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c21(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c21(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c21(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c21(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c21(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c21(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c21(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(s(z0), x1)) -> c21(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c21(MARK(x0)) MARK(first(x0, s(z0))) -> c21(MARK(x0)) MARK(first(x0, 0)) -> c21(MARK(x0)) MARK(first(x0, nil)) -> c21(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c21(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c21(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c22(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c22(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c22(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c22(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c22(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c22(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c22(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c22(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c22(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c22(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c22(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c22(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c22(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c22(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c22(MARK(x1)) MARK(first(recip(z0), x1)) -> c22(MARK(x1)) MARK(first(0, x1)) -> c22(MARK(x1)) MARK(first(nil, x1)) -> c22(MARK(x1)) 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(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(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, 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(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(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, 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(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__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(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(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(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(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, 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(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(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, 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(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)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c18(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c18(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c18(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c18(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c18(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c18(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c18(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c18(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c18(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c18(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(s(z0), x1)) -> c18(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c18(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c18(MARK(recip(z0))) MARK(add(0, x1)) -> c18(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c19(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c19(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c19(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c19(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c19(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c19(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c19(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c19(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c19(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c19(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c19(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c19(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c19(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c19(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c19(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c19(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c19(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c19(MARK(x1)) MARK(add(recip(z0), x1)) -> c19(MARK(x1)) MARK(add(nil, x1)) -> c19(MARK(x1)) MARK(dbl(terms(z0))) -> c20(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c20(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c20(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c20(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c20(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(s(z0))) -> c20(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c20(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c20(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c21(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c21(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c21(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c21(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c21(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c21(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c21(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c21(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c21(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c21(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c21(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(s(z0), x1)) -> c21(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c21(MARK(x0)) MARK(first(x0, s(z0))) -> c21(MARK(x0)) MARK(first(x0, 0)) -> c21(MARK(x0)) MARK(first(x0, nil)) -> c21(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c21(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c21(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c22(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c22(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c22(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c22(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c22(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c22(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c22(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c22(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c22(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c22(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c22(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c22(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c22(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c22(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c22(MARK(x1)) MARK(first(recip(z0), x1)) -> c22(MARK(x1)) MARK(first(0, x1)) -> c22(MARK(x1)) MARK(first(nil, x1)) -> c22(MARK(x1)) 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(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(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, 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(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(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, 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(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__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(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(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(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(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, 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(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(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, 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(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, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c23_1, c24_1, c25_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, c16_2, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1 ---------------------------------------- (137) 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(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))) ---------------------------------------- (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) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(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)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c18(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c18(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c18(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c18(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c18(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c18(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c18(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c18(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c18(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c18(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(s(z0), x1)) -> c18(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c18(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c18(MARK(recip(z0))) MARK(add(0, x1)) -> c18(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c19(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c19(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c19(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c19(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c19(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c19(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c19(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c19(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c19(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c19(A__ADD(a__sqr(mark(z0)), mark(x1)), 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MARK(dbl(s(z0))) -> c20(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c20(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c20(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c21(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c21(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c21(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c21(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c21(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c21(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c21(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c21(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c21(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c21(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c21(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(s(z0), x1)) -> c21(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c21(MARK(x0)) MARK(first(x0, s(z0))) -> c21(MARK(x0)) MARK(first(x0, 0)) -> c21(MARK(x0)) MARK(first(x0, nil)) -> c21(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c21(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c21(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c22(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c22(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c22(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c22(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c22(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c22(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c22(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c22(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c22(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c22(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c22(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c22(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c22(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c22(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c22(MARK(x1)) MARK(first(recip(z0), x1)) -> c22(MARK(x1)) MARK(first(0, x1)) -> c22(MARK(x1)) MARK(first(nil, x1)) -> c22(MARK(x1)) 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(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(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, 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(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(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, 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(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__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(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(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(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(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, 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(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(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, 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(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(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(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)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c18(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c18(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c18(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c18(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c18(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c18(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c18(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c18(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c18(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c18(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(s(z0), x1)) -> c18(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c18(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c18(MARK(recip(z0))) MARK(add(0, x1)) -> c18(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c19(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c19(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c19(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c19(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c19(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c19(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c19(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c19(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c19(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c19(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c19(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c19(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c19(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c19(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c19(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c19(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c19(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c19(MARK(x1)) MARK(add(recip(z0), x1)) -> c19(MARK(x1)) MARK(add(nil, x1)) -> c19(MARK(x1)) MARK(dbl(terms(z0))) -> c20(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c20(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c20(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c20(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c20(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(s(z0))) -> c20(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c20(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c20(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c21(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c21(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c21(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c21(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c21(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c21(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c21(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c21(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c21(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c21(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c21(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(s(z0), x1)) -> c21(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c21(MARK(x0)) MARK(first(x0, s(z0))) -> c21(MARK(x0)) MARK(first(x0, 0)) -> c21(MARK(x0)) MARK(first(x0, nil)) -> c21(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c21(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c21(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c22(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c22(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c22(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c22(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c22(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c22(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c22(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c22(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c22(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c22(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c22(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c22(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c22(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c22(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c22(MARK(x1)) MARK(first(recip(z0), x1)) -> c22(MARK(x1)) MARK(first(0, x1)) -> c22(MARK(x1)) MARK(first(nil, x1)) -> c22(MARK(x1)) 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(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(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, 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(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(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, 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(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__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(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(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(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(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, 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(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(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, 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(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(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(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, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c23_1, c24_1, c25_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, c16_2, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1 ---------------------------------------- (139) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 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) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(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)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c18(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c18(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c18(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c18(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c18(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c18(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c18(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c18(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c18(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c18(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(s(z0), x1)) -> c18(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c18(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c18(MARK(recip(z0))) MARK(add(0, x1)) -> c18(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c19(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c19(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c19(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c19(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c19(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c19(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c19(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c19(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c19(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c19(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c19(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c19(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c19(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c19(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c19(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c19(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c19(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c19(MARK(x1)) MARK(add(recip(z0), x1)) -> c19(MARK(x1)) MARK(add(nil, x1)) -> c19(MARK(x1)) MARK(dbl(terms(z0))) -> c20(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c20(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c20(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c20(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c20(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(s(z0))) -> c20(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c20(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c20(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c21(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c21(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c21(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c21(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c21(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c21(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c21(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c21(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c21(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c21(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c21(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(s(z0), x1)) -> c21(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c21(MARK(x0)) MARK(first(x0, s(z0))) -> c21(MARK(x0)) MARK(first(x0, 0)) -> c21(MARK(x0)) MARK(first(x0, nil)) -> c21(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c21(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c21(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c22(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c22(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c22(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c22(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c22(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c22(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c22(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c22(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c22(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c22(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c22(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c22(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c22(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c22(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c22(MARK(x1)) MARK(first(recip(z0), x1)) -> c22(MARK(x1)) MARK(first(0, x1)) -> c22(MARK(x1)) MARK(first(nil, x1)) -> c22(MARK(x1)) 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(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(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, 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(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(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, 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(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__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(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(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(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(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, 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(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(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, 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(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(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(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)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c18(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c18(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c18(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c18(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c18(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c18(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c18(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c18(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c18(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c18(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(s(z0), x1)) -> c18(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c18(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c18(MARK(recip(z0))) MARK(add(0, x1)) -> c18(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c19(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c19(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c19(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c19(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c19(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c19(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c19(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c19(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c19(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c19(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c19(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c19(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c19(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c19(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c19(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c19(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c19(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c19(MARK(x1)) MARK(add(recip(z0), x1)) -> c19(MARK(x1)) MARK(add(nil, x1)) -> c19(MARK(x1)) MARK(dbl(terms(z0))) -> c20(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c20(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c20(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c20(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c20(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(s(z0))) -> c20(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c20(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c20(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c21(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c21(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c21(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c21(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c21(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c21(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c21(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c21(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c21(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c21(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c21(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(s(z0), x1)) -> c21(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c21(MARK(x0)) MARK(first(x0, s(z0))) -> c21(MARK(x0)) MARK(first(x0, 0)) -> c21(MARK(x0)) MARK(first(x0, nil)) -> c21(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c21(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c21(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c22(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c22(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c22(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c22(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c22(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c22(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c22(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c22(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c22(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c22(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c22(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c22(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c22(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c22(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c22(MARK(x1)) MARK(first(recip(z0), x1)) -> c22(MARK(x1)) MARK(first(0, x1)) -> c22(MARK(x1)) MARK(first(nil, x1)) -> c22(MARK(x1)) 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(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(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, 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(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(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, 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(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__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(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(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(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(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, 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(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(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, 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(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(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(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, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c23_1, c24_1, c25_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, c16_2, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1 ---------------------------------------- (141) 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(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))) ---------------------------------------- (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) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(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)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, 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MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c22(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c22(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c22(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c22(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c22(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c22(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c22(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c22(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c22(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c22(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c22(MARK(x1)) MARK(first(recip(z0), x1)) -> c22(MARK(x1)) MARK(first(0, x1)) -> c22(MARK(x1)) MARK(first(nil, x1)) -> c22(MARK(x1)) 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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(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, 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), 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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, 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(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__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(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(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(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(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, 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(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(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, 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(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(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(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(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)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c18(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c18(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c18(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c18(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c18(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c18(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c18(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c18(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c18(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c18(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(s(z0), x1)) -> c18(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c18(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c18(MARK(recip(z0))) MARK(add(0, x1)) -> c18(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c19(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c19(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c19(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c19(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c19(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c19(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c19(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c19(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c19(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c19(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c19(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c19(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c19(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c19(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c19(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c19(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c19(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c19(MARK(x1)) MARK(add(recip(z0), x1)) -> c19(MARK(x1)) MARK(add(nil, x1)) -> c19(MARK(x1)) MARK(dbl(terms(z0))) -> c20(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c20(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c20(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c20(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c20(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(s(z0))) -> c20(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c20(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c20(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c21(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c21(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c21(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c21(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c21(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c21(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c21(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c21(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c21(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c21(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c21(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(s(z0), x1)) -> c21(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c21(MARK(x0)) MARK(first(x0, s(z0))) -> c21(MARK(x0)) MARK(first(x0, 0)) -> c21(MARK(x0)) MARK(first(x0, nil)) -> c21(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c21(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c21(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c22(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c22(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c22(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c22(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c22(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c22(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c22(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c22(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c22(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c22(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c22(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c22(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c22(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c22(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c22(MARK(x1)) MARK(first(recip(z0), x1)) -> c22(MARK(x1)) MARK(first(0, x1)) -> c22(MARK(x1)) MARK(first(nil, x1)) -> c22(MARK(x1)) 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(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(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, 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(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(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, 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(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__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(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(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(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(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, 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(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(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, 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(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(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(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(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, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c23_1, c24_1, c25_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, c16_2, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_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) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(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)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c18(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c18(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c18(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c18(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c18(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c18(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c18(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c18(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c18(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c18(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(s(z0), x1)) -> c18(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c18(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c18(MARK(recip(z0))) MARK(add(0, x1)) -> c18(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c19(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c19(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c19(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c19(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c19(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c19(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c19(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c19(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c19(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c19(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c19(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c19(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c19(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c19(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c19(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c19(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c19(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c19(MARK(x1)) MARK(add(recip(z0), x1)) -> c19(MARK(x1)) MARK(add(nil, x1)) -> c19(MARK(x1)) MARK(dbl(terms(z0))) -> c20(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c20(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c20(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c20(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c20(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(s(z0))) -> c20(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c20(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c20(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c21(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c21(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c21(A__FIRST(mark(x0), a__add(mark(z0), 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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, 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, 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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__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))) 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z1))), MARK(first(z0, z1))) 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(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(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, 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(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(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, 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(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(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(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(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)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c18(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c18(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c18(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c18(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c18(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c18(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c18(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c18(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c18(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c18(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(s(z0), x1)) -> c18(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c18(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c18(MARK(recip(z0))) MARK(add(0, x1)) -> c18(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c19(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c19(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c19(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c19(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c19(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c19(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c19(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c19(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c19(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c19(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c19(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c19(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c19(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c19(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c19(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c19(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c19(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c19(MARK(x1)) MARK(add(recip(z0), x1)) -> c19(MARK(x1)) MARK(add(nil, x1)) -> c19(MARK(x1)) MARK(dbl(terms(z0))) -> c20(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c20(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c20(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c20(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c20(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(s(z0))) -> c20(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c20(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c20(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c21(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c21(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c21(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c21(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c21(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c21(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c21(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c21(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c21(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c21(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c21(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(s(z0), x1)) -> c21(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c21(MARK(x0)) MARK(first(x0, s(z0))) -> c21(MARK(x0)) MARK(first(x0, 0)) -> c21(MARK(x0)) MARK(first(x0, nil)) -> c21(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c21(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c21(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c22(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c22(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c22(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c22(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c22(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c22(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c22(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c22(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c22(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c22(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c22(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c22(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c22(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c22(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c22(MARK(x1)) MARK(first(recip(z0), x1)) -> c22(MARK(x1)) MARK(first(0, x1)) -> c22(MARK(x1)) MARK(first(nil, x1)) -> c22(MARK(x1)) 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(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(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, 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(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, 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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, 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(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__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(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(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(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(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, 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(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(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, 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(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(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(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(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, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c23_1, c24_1, c25_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, c16_2, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1 ---------------------------------------- (145) 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(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))) ---------------------------------------- (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) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(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)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c18(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c18(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c18(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c18(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c18(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c18(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c18(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c18(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c18(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c18(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(s(z0), x1)) -> c18(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c18(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c18(MARK(recip(z0))) MARK(add(0, x1)) -> c18(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c19(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c19(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c19(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c19(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c19(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c19(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c19(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c19(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c19(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c19(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c19(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c19(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c19(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c19(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c19(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c19(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c19(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c19(MARK(x1)) MARK(add(recip(z0), x1)) -> c19(MARK(x1)) MARK(add(nil, x1)) -> c19(MARK(x1)) MARK(dbl(terms(z0))) -> c20(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c20(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c20(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c20(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c20(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(s(z0))) -> c20(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c20(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c20(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c21(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c21(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c21(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c21(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c21(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c21(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c21(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c21(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c21(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c21(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c21(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(s(z0), x1)) -> c21(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c21(MARK(x0)) MARK(first(x0, s(z0))) -> c21(MARK(x0)) MARK(first(x0, 0)) -> c21(MARK(x0)) MARK(first(x0, nil)) -> c21(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c21(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c21(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c22(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c22(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c22(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c22(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c22(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c22(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c22(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c22(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c22(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) 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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, 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(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)), 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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, 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(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__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(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(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(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(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, 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(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(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, 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(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(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(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(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(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)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c18(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c18(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c18(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c18(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c18(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c18(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c18(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c18(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c18(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c18(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(s(z0), x1)) -> c18(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c18(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c18(MARK(recip(z0))) MARK(add(0, x1)) -> c18(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c19(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c19(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c19(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c19(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c19(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c19(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c19(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c19(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c19(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c19(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c19(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c19(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c19(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c19(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c19(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c19(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c19(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c19(MARK(x1)) MARK(add(recip(z0), x1)) -> c19(MARK(x1)) MARK(add(nil, x1)) -> c19(MARK(x1)) MARK(dbl(terms(z0))) -> c20(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c20(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c20(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c20(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c20(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(s(z0))) -> c20(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c20(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c20(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c21(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c21(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c21(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c21(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c21(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c21(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c21(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c21(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c21(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c21(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c21(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(s(z0), x1)) -> c21(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c21(MARK(x0)) MARK(first(x0, s(z0))) -> c21(MARK(x0)) MARK(first(x0, 0)) -> c21(MARK(x0)) MARK(first(x0, nil)) -> c21(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c21(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c21(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c22(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c22(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c22(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c22(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c22(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c22(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c22(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c22(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c22(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c22(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c22(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c22(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c22(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c22(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c22(MARK(x1)) MARK(first(recip(z0), x1)) -> c22(MARK(x1)) MARK(first(0, x1)) -> c22(MARK(x1)) MARK(first(nil, x1)) -> c22(MARK(x1)) 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(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(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, 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(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(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, 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(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__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(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(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(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(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, 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(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(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, 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(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(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(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(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(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, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c23_1, c24_1, c25_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, c16_2, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1 ---------------------------------------- (147) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 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) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(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)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c18(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c18(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c18(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c18(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c18(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c18(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c18(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c18(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c18(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c18(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(s(z0), x1)) -> c18(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c18(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c18(MARK(recip(z0))) MARK(add(0, x1)) -> c18(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c19(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c19(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c19(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c19(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c19(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c19(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c19(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c19(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c19(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c19(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c19(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c19(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c19(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c19(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c19(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c19(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c19(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c19(MARK(x1)) MARK(add(recip(z0), x1)) -> c19(MARK(x1)) MARK(add(nil, x1)) -> c19(MARK(x1)) MARK(dbl(terms(z0))) -> c20(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c20(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c20(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c20(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c20(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(s(z0))) -> c20(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c20(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c20(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c21(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c21(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c21(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c21(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c21(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c21(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c21(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c21(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c21(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c21(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c21(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(s(z0), x1)) -> c21(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c21(MARK(x0)) MARK(first(x0, s(z0))) -> c21(MARK(x0)) MARK(first(x0, 0)) -> c21(MARK(x0)) MARK(first(x0, nil)) -> c21(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c21(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c21(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c22(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c22(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c22(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c22(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c22(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c22(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c22(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c22(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c22(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c22(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c22(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c22(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c22(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c22(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c22(MARK(x1)) MARK(first(recip(z0), x1)) -> c22(MARK(x1)) MARK(first(0, x1)) -> c22(MARK(x1)) MARK(first(nil, x1)) -> c22(MARK(x1)) 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(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(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, 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), 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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(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, 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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(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__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(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(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(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(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, 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(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(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, 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(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(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(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(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(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)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> 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MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c18(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c18(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c18(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c18(A__ADD(mark(x0), 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MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c19(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c19(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c19(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c19(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c19(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c19(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c19(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c19(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c19(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c19(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c19(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c19(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c19(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c19(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c19(MARK(x1)) MARK(add(recip(z0), x1)) -> c19(MARK(x1)) MARK(add(nil, x1)) -> c19(MARK(x1)) MARK(dbl(terms(z0))) -> c20(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c20(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c20(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c20(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c20(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(s(z0))) -> c20(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c20(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c20(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c21(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c21(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c21(A__FIRST(mark(x0), a__add(mark(z0), 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MARK(first(cons(z0, z1), x1)) -> c21(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c21(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c22(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c22(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c22(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c22(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c22(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c22(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c22(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c22(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c22(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c22(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c22(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c22(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c22(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c22(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c22(MARK(x1)) MARK(first(recip(z0), x1)) -> c22(MARK(x1)) MARK(first(0, x1)) -> c22(MARK(x1)) MARK(first(nil, x1)) -> c22(MARK(x1)) 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(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(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, 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(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(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, 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(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__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(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(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(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(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, 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(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(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, 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(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(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(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(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(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, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c23_1, c24_1, c25_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, c16_2, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1 ---------------------------------------- (149) 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(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))) ---------------------------------------- (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) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(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)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c18(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c18(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c18(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c18(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c18(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c18(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c18(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c18(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c18(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c18(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(s(z0), x1)) -> c18(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c18(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c18(MARK(recip(z0))) MARK(add(0, x1)) -> c18(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c19(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c19(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c19(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c19(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c19(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c19(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c19(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c19(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c19(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c19(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c19(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c19(A__ADD(a__dbl(mark(z0)), mark(x1)), 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x1)) -> c22(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c22(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c22(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c22(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c22(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c22(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c22(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c22(MARK(x1)) MARK(first(recip(z0), x1)) -> c22(MARK(x1)) MARK(first(0, x1)) -> c22(MARK(x1)) MARK(first(nil, x1)) -> c22(MARK(x1)) 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))) -> 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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(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(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, 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(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__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(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(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(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(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, 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(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(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, 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(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(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(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(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(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(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)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c18(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c18(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c18(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c18(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c18(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c18(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c18(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c18(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c18(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c18(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(s(z0), x1)) -> c18(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c18(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c18(MARK(recip(z0))) MARK(add(0, x1)) -> c18(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c19(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c19(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c19(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c19(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c19(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c19(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c19(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c19(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c19(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c19(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c19(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c19(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c19(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c19(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c19(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c19(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c19(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c19(MARK(x1)) MARK(add(recip(z0), x1)) -> c19(MARK(x1)) MARK(add(nil, x1)) -> c19(MARK(x1)) MARK(dbl(terms(z0))) -> c20(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c20(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c20(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c20(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c20(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(s(z0))) -> c20(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c20(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c20(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c21(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c21(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c21(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c21(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c21(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c21(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c21(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c21(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c21(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c21(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c21(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(s(z0), x1)) -> c21(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c21(MARK(x0)) MARK(first(x0, s(z0))) -> c21(MARK(x0)) MARK(first(x0, 0)) -> c21(MARK(x0)) MARK(first(x0, nil)) -> c21(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c21(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c21(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c22(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c22(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c22(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c22(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c22(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c22(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c22(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c22(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c22(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c22(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c22(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c22(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c22(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c22(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c22(MARK(x1)) MARK(first(recip(z0), x1)) -> c22(MARK(x1)) MARK(first(0, x1)) -> c22(MARK(x1)) MARK(first(nil, x1)) -> c22(MARK(x1)) 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(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(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, 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(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(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, 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(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__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(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(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(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(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, 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(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(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, 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(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(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(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(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(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(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, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c23_1, c24_1, c25_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, c16_2, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1 ---------------------------------------- (151) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 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) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(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)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c18(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c18(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c18(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c18(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c18(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c18(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c18(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c18(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c18(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c18(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(s(z0), x1)) -> c18(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c18(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c18(MARK(recip(z0))) MARK(add(0, x1)) -> c18(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c19(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c19(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c19(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c19(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c19(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c19(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c19(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c19(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c19(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c19(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c19(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c19(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c19(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c19(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c19(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c19(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c19(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c19(MARK(x1)) MARK(add(recip(z0), x1)) -> c19(MARK(x1)) MARK(add(nil, x1)) -> c19(MARK(x1)) MARK(dbl(terms(z0))) -> c20(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c20(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c20(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c20(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c20(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(s(z0))) -> c20(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c20(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c20(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c21(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c21(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c21(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c21(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c21(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c21(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c21(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c21(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c21(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c21(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c21(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(s(z0), x1)) -> c21(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c21(MARK(x0)) MARK(first(x0, s(z0))) -> c21(MARK(x0)) MARK(first(x0, 0)) -> c21(MARK(x0)) MARK(first(x0, nil)) -> c21(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c21(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c21(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c22(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c22(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c22(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c22(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c22(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c22(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c22(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c22(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c22(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c22(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c22(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c22(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c22(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c22(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c22(MARK(x1)) MARK(first(recip(z0), x1)) -> c22(MARK(x1)) MARK(first(0, x1)) -> c22(MARK(x1)) MARK(first(nil, x1)) -> c22(MARK(x1)) 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(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(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, 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(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(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, 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(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__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(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(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(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(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, 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(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(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, 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(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(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(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(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(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(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)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c18(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c18(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c18(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c18(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c18(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c18(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c18(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c18(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c18(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c18(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(s(z0), x1)) -> c18(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c18(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c18(MARK(recip(z0))) MARK(add(0, x1)) -> c18(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c19(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c19(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c19(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c19(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c19(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c19(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c19(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c19(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c19(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c19(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c19(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c19(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c19(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c19(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c19(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c19(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c19(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c19(MARK(x1)) MARK(add(recip(z0), x1)) -> c19(MARK(x1)) MARK(add(nil, x1)) -> c19(MARK(x1)) MARK(dbl(terms(z0))) -> c20(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c20(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c20(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c20(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c20(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(s(z0))) -> c20(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c20(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c20(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c21(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c21(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c21(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c21(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c21(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c21(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c21(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c21(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c21(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c21(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c21(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(s(z0), x1)) -> c21(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c21(MARK(x0)) MARK(first(x0, s(z0))) -> c21(MARK(x0)) MARK(first(x0, 0)) -> c21(MARK(x0)) MARK(first(x0, nil)) -> c21(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c21(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c21(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c22(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c22(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c22(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), 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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(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)))) 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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(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__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(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(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(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(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, 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(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(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, 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(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(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(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(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(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(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, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c23_1, c24_1, c25_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, c16_2, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1 ---------------------------------------- (153) 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(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))) ---------------------------------------- (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) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(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)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c18(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c18(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c18(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c18(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c18(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c18(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c18(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c18(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c18(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c18(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(s(z0), x1)) -> c18(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c18(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c18(MARK(recip(z0))) MARK(add(0, x1)) -> c18(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c19(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c19(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c19(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c19(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c19(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c19(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c19(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c19(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c19(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c19(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c19(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c19(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c19(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c19(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c19(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c19(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c19(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c19(MARK(x1)) MARK(add(recip(z0), x1)) -> c19(MARK(x1)) MARK(add(nil, x1)) -> c19(MARK(x1)) MARK(dbl(terms(z0))) -> c20(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c20(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c20(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c20(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c20(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(s(z0))) -> c20(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c20(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c20(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c21(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c21(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c21(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c21(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c21(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c21(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c21(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c21(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c21(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c21(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c21(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(s(z0), x1)) -> c21(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c21(MARK(x0)) MARK(first(x0, s(z0))) -> c21(MARK(x0)) MARK(first(x0, 0)) -> c21(MARK(x0)) MARK(first(x0, nil)) -> c21(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c21(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c21(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c22(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c22(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c22(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c22(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c22(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c22(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c22(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c22(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c22(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c22(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c22(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c22(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c22(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c22(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c22(MARK(x1)) MARK(first(recip(z0), x1)) -> c22(MARK(x1)) MARK(first(0, x1)) -> c22(MARK(x1)) MARK(first(nil, x1)) -> c22(MARK(x1)) 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(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(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, 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(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(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, 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(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__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(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(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(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(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, 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(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(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, 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(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(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(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(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(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(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(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)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c18(A__ADD(mark(x0), cons(mark(z0), 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a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c19(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c19(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c19(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c19(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c19(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c19(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c19(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c19(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c19(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c19(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c19(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c19(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c19(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c19(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c19(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c19(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c19(MARK(x1)) MARK(add(recip(z0), x1)) -> c19(MARK(x1)) MARK(add(nil, x1)) -> c19(MARK(x1)) MARK(dbl(terms(z0))) -> c20(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c20(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c20(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c20(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c20(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(s(z0))) -> c20(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c20(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c20(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c21(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c21(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c21(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c21(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c21(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c21(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c21(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c21(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c21(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c21(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c21(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(s(z0), x1)) -> c21(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c21(MARK(x0)) MARK(first(x0, s(z0))) -> c21(MARK(x0)) MARK(first(x0, 0)) -> c21(MARK(x0)) MARK(first(x0, nil)) -> c21(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c21(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c21(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c22(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c22(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c22(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c22(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c22(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c22(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c22(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c22(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c22(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c22(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c22(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c22(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c22(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c22(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c22(MARK(x1)) MARK(first(recip(z0), x1)) -> c22(MARK(x1)) MARK(first(0, x1)) -> c22(MARK(x1)) MARK(first(nil, x1)) -> c22(MARK(x1)) 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(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), 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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(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(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, 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(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__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(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(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(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(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, 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(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(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, 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(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(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(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(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(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(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(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, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c23_1, c24_1, c25_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, c16_2, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_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) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(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)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c18(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c18(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c18(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c18(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c18(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c18(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c18(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c18(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c18(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c18(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(s(z0), x1)) -> c18(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c18(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c18(MARK(recip(z0))) MARK(add(0, x1)) -> c18(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c19(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c19(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c19(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c19(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c19(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c19(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c19(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c19(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c19(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c19(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c19(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c19(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c19(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c19(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c19(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c19(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c19(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c19(MARK(x1)) MARK(add(recip(z0), x1)) -> c19(MARK(x1)) MARK(add(nil, x1)) -> c19(MARK(x1)) MARK(dbl(terms(z0))) -> c20(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c20(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c20(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c20(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c20(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(s(z0))) -> c20(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c20(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c20(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c21(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c21(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c21(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c21(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c21(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c21(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c21(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c21(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c21(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c21(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c21(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(s(z0), x1)) -> c21(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c21(MARK(x0)) MARK(first(x0, s(z0))) -> c21(MARK(x0)) MARK(first(x0, 0)) -> c21(MARK(x0)) MARK(first(x0, nil)) -> c21(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c21(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c21(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c22(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c22(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c22(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c22(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c22(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c22(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c22(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c22(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c22(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c22(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c22(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c22(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c22(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c22(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c22(MARK(x1)) MARK(first(recip(z0), x1)) -> c22(MARK(x1)) MARK(first(0, x1)) -> c22(MARK(x1)) MARK(first(nil, x1)) -> c22(MARK(x1)) 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(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(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, 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(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(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, 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(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__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(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(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(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(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, 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(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(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, 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(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(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(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(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(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(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(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)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c18(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c18(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c18(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c18(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c18(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c18(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c18(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c18(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c18(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c18(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(s(z0), x1)) -> c18(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c18(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c18(MARK(recip(z0))) MARK(add(0, x1)) -> c18(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c19(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c19(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c19(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c19(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c19(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c19(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c19(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c19(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c19(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c19(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c19(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c19(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c19(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c19(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c19(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c19(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c19(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c19(MARK(x1)) MARK(add(recip(z0), x1)) -> c19(MARK(x1)) MARK(add(nil, x1)) -> c19(MARK(x1)) MARK(dbl(terms(z0))) -> c20(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c20(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c20(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c20(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c20(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(s(z0))) -> c20(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c20(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c20(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c21(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c21(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c21(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c21(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c21(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c21(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c21(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c21(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c21(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c21(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c21(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(s(z0), x1)) -> c21(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c21(MARK(x0)) MARK(first(x0, s(z0))) -> c21(MARK(x0)) MARK(first(x0, 0)) -> c21(MARK(x0)) MARK(first(x0, nil)) -> c21(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c21(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c21(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c22(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c22(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c22(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c22(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c22(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c22(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c22(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c22(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c22(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c22(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c22(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c22(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c22(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c22(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c22(MARK(x1)) MARK(first(recip(z0), x1)) -> c22(MARK(x1)) MARK(first(0, x1)) -> c22(MARK(x1)) MARK(first(nil, x1)) -> c22(MARK(x1)) 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(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(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, 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(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(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, 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(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__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(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(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(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(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, 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(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(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, 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(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(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(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(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(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(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(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, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c23_1, c24_1, c25_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, c16_2, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1 ---------------------------------------- (157) 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, 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(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))) ---------------------------------------- (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) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(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)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c18(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c18(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c18(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c18(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c18(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c18(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c18(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c18(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c18(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c18(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(s(z0), x1)) -> c18(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c18(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c18(MARK(recip(z0))) MARK(add(0, x1)) -> c18(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c19(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c19(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c19(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c19(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c19(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c19(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c19(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c19(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c19(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c19(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c19(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c19(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c19(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c19(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c19(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c19(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c19(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c19(MARK(x1)) MARK(add(recip(z0), x1)) -> c19(MARK(x1)) MARK(add(nil, x1)) -> c19(MARK(x1)) MARK(dbl(terms(z0))) -> c20(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c20(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c20(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c20(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c20(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(s(z0))) -> c20(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c20(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c20(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c21(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c21(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c21(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c21(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c21(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c21(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c21(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c21(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c21(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c21(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c21(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(s(z0), x1)) -> c21(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c21(MARK(x0)) MARK(first(x0, s(z0))) -> c21(MARK(x0)) MARK(first(x0, 0)) -> c21(MARK(x0)) MARK(first(x0, nil)) -> c21(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c21(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c21(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c22(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c22(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c22(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c22(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c22(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c22(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c22(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c22(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c22(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c22(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c22(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c22(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c22(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c22(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c22(MARK(x1)) MARK(first(recip(z0), x1)) -> c22(MARK(x1)) MARK(first(0, x1)) -> c22(MARK(x1)) MARK(first(nil, x1)) -> c22(MARK(x1)) 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(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(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, 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(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(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, 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(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__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(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(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(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(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, 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(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(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, 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(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(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(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(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(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(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(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, 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(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)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c18(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c18(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c18(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c18(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c18(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c18(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c18(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c18(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c18(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c18(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(s(z0), x1)) -> c18(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c18(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c18(MARK(recip(z0))) MARK(add(0, x1)) -> c18(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c19(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c19(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c19(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c19(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c19(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c19(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c19(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c19(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c19(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c19(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c19(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c19(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c19(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c19(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c19(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c19(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c19(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c19(MARK(x1)) MARK(add(recip(z0), x1)) -> c19(MARK(x1)) MARK(add(nil, x1)) -> c19(MARK(x1)) MARK(dbl(terms(z0))) -> c20(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c20(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c20(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c20(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c20(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(s(z0))) -> c20(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c20(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c20(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c21(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c21(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c21(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c21(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c21(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c21(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c21(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c21(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c21(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c21(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c21(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(s(z0), x1)) -> c21(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c21(MARK(x0)) MARK(first(x0, s(z0))) -> c21(MARK(x0)) MARK(first(x0, 0)) -> c21(MARK(x0)) MARK(first(x0, nil)) -> c21(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c21(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c21(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c22(A__FIRST(mark(x0), a__terms(mark(z0))), 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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__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(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))) 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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(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(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, 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(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(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, 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(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(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(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(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(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(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(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, 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(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, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c23_1, c24_1, c25_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, c16_2, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_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) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(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)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c18(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c18(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c18(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c18(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c18(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c18(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c18(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c18(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c18(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c18(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(s(z0), x1)) -> c18(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c18(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c18(MARK(recip(z0))) MARK(add(0, x1)) -> c18(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c19(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c19(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c19(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c19(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c19(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c19(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c19(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c19(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c19(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c19(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c19(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c19(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c19(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c19(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c19(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c19(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c19(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c19(MARK(x1)) MARK(add(recip(z0), x1)) -> c19(MARK(x1)) MARK(add(nil, x1)) -> c19(MARK(x1)) MARK(dbl(terms(z0))) -> c20(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c20(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c20(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c20(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c20(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(s(z0))) -> c20(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c20(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c20(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c21(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c21(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c21(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c21(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c21(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c21(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c21(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c21(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c21(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c21(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c21(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(s(z0), x1)) -> c21(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c21(MARK(x0)) MARK(first(x0, s(z0))) -> c21(MARK(x0)) MARK(first(x0, 0)) -> c21(MARK(x0)) MARK(first(x0, nil)) -> c21(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c21(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c21(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c22(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c22(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c22(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c22(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c22(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c22(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c22(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c22(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c22(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c22(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c22(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c22(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c22(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c22(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c22(MARK(x1)) MARK(first(recip(z0), x1)) -> c22(MARK(x1)) MARK(first(0, x1)) -> c22(MARK(x1)) MARK(first(nil, x1)) -> c22(MARK(x1)) 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(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(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, 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(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(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, 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(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__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(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(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(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(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, 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(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(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, 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(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(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(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(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(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(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(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, 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(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)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c18(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c18(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c18(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c18(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c18(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c18(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c18(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c18(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c18(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c18(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(s(z0), x1)) -> c18(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c18(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c18(MARK(recip(z0))) MARK(add(0, x1)) -> c18(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c19(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c19(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c19(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c19(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c19(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c19(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c19(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c19(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c19(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c19(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c19(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c19(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c19(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c19(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c19(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c19(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c19(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c19(MARK(x1)) MARK(add(recip(z0), x1)) -> c19(MARK(x1)) MARK(add(nil, x1)) -> c19(MARK(x1)) MARK(dbl(terms(z0))) -> c20(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c20(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c20(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c20(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c20(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(s(z0))) -> c20(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c20(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c20(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c21(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c21(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c21(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c21(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c21(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c21(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c21(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c21(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c21(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c21(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c21(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(s(z0), x1)) -> c21(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c21(MARK(x0)) MARK(first(x0, s(z0))) -> c21(MARK(x0)) MARK(first(x0, 0)) -> c21(MARK(x0)) MARK(first(x0, nil)) -> c21(MARK(x0)) 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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(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(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, 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(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(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, 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(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(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(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(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(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(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(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, 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(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, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c23_1, c24_1, c25_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, c16_2, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1 ---------------------------------------- (161) 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(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))) ---------------------------------------- (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) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(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)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c18(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c18(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c18(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c18(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c18(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c18(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c18(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c18(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c18(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c18(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(s(z0), x1)) -> c18(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c18(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c18(MARK(recip(z0))) MARK(add(0, x1)) -> c18(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c19(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c19(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c19(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c19(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c19(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> 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c22(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c22(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c22(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c22(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c22(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c22(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c22(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c22(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c22(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c22(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c22(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c22(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c22(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c22(MARK(x1)) MARK(first(recip(z0), x1)) -> c22(MARK(x1)) MARK(first(0, x1)) -> c22(MARK(x1)) MARK(first(nil, x1)) -> c22(MARK(x1)) 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(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(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, 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(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(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, 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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(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__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(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(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(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(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, 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(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(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, 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(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(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(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(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(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(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(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, 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(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(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)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), 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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, 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(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__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(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(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(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(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, 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(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(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, 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(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(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(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(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(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(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(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, 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(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(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, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c23_1, c24_1, c25_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, c16_2, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1 ---------------------------------------- (163) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (164) Obligation: Complexity Dependency Tuples Problem Rules: a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0) -> 0 a__sqr(s(z0)) -> s(a__add(a__sqr(mark(z0)), a__dbl(mark(z0)))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(a__dbl(mark(z0)))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(a__add(mark(z0), mark(z1))) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(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)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), 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MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c19(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c19(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c19(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c19(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c19(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c19(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c19(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c19(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c19(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c19(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c19(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c19(A__ADD(0, mark(x1)), MARK(x1)) 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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, 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(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(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, 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(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__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(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(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(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(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, 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(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(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, 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(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(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(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(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(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(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(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, 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(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(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)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(cons(z0, z1))) -> c3(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__SQR(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__SQR(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__SQR(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c18(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c18(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c18(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c18(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c18(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c18(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c18(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c18(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c18(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c18(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(s(z0), x1)) -> c18(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c18(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c18(MARK(recip(z0))) MARK(add(0, x1)) -> c18(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c19(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c19(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c19(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c19(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c19(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c19(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c19(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c19(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c19(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c19(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c19(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c19(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c19(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c19(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c19(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c19(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c19(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c19(MARK(x1)) MARK(add(recip(z0), x1)) -> c19(MARK(x1)) MARK(add(nil, x1)) -> c19(MARK(x1)) MARK(dbl(terms(z0))) -> c20(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c20(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c20(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c20(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c20(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(s(z0))) -> c20(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c20(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c20(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c21(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c21(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c21(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c21(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c21(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c21(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c21(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c21(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c21(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c21(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c21(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(s(z0), x1)) -> c21(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c21(MARK(x0)) MARK(first(x0, s(z0))) -> c21(MARK(x0)) MARK(first(x0, 0)) -> c21(MARK(x0)) MARK(first(x0, nil)) -> c21(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c21(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c21(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c22(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c22(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c22(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c22(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c22(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c22(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c22(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c22(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c22(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c22(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c22(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c22(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c22(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c22(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c22(MARK(x1)) MARK(first(recip(z0), x1)) -> c22(MARK(x1)) MARK(first(0, x1)) -> c22(MARK(x1)) MARK(first(nil, x1)) -> c22(MARK(x1)) 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(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(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, 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(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(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, 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(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__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(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(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(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(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, 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(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(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, 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(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(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(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(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(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(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(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, 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(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(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, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c23_1, c24_1, c25_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, c16_2, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1 ---------------------------------------- (165) 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, 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(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))) ---------------------------------------- (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) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(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)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c18(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c18(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c18(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c18(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c18(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c18(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c18(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c18(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c18(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c18(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(s(z0), x1)) -> c18(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c18(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c18(MARK(recip(z0))) MARK(add(0, x1)) -> c18(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c19(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c19(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c19(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c19(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c19(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c19(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c19(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c19(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c19(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c19(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c19(A__ADD(a__add(mark(z0), mark(z1)), 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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(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(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(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(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, 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(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(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, 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(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(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(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(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(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(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(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, 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(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(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, 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(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)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> 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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, 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(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(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, 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(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__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(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(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(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(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, 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(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(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, 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(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(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(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(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(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(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(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, 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(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(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, 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(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, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c23_1, c24_1, c25_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, c16_2, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_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) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(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)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c18(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c18(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c18(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c18(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c18(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c18(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c18(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c18(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c18(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c18(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(s(z0), x1)) -> c18(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c18(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c18(MARK(recip(z0))) MARK(add(0, x1)) -> c18(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c19(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c19(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c19(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c19(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c19(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c19(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c19(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c19(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c19(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c19(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c19(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c19(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c19(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c19(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c19(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c19(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c19(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c19(MARK(x1)) MARK(add(recip(z0), x1)) -> c19(MARK(x1)) MARK(add(nil, x1)) -> c19(MARK(x1)) MARK(dbl(terms(z0))) -> c20(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c20(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c20(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c20(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c20(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(s(z0))) -> c20(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c20(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c20(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c21(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c21(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c21(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c21(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c21(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c21(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c21(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c21(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c21(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c21(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c21(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(s(z0), x1)) -> c21(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c21(MARK(x0)) MARK(first(x0, s(z0))) -> c21(MARK(x0)) MARK(first(x0, 0)) -> 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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__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(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))), 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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(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(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, 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(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(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, 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(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(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(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(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(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(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(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, 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(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(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, 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(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)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c18(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c18(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c18(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c18(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c18(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c18(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c18(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c18(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c18(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c18(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(s(z0), x1)) -> c18(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c18(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c18(MARK(recip(z0))) MARK(add(0, x1)) -> c18(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c19(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c19(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c19(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c19(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c19(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c19(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c19(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c19(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c19(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c19(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c19(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c19(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c19(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c19(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c19(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c19(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c19(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c19(MARK(x1)) MARK(add(recip(z0), x1)) -> c19(MARK(x1)) MARK(add(nil, x1)) -> c19(MARK(x1)) MARK(dbl(terms(z0))) -> c20(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c20(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c20(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c20(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c20(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(s(z0))) -> c20(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c20(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c20(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c21(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c21(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c21(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c21(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c21(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c21(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c21(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c21(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c21(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c21(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c21(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(s(z0), x1)) -> c21(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c21(MARK(x0)) MARK(first(x0, s(z0))) -> c21(MARK(x0)) MARK(first(x0, 0)) -> c21(MARK(x0)) MARK(first(x0, nil)) -> c21(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c21(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c21(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c22(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c22(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c22(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c22(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c22(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c22(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c22(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c22(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c22(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c22(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c22(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c22(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c22(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c22(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c22(MARK(x1)) MARK(first(recip(z0), x1)) -> c22(MARK(x1)) MARK(first(0, x1)) -> c22(MARK(x1)) MARK(first(nil, x1)) -> c22(MARK(x1)) 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(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(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, 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(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(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, 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(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__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(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(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(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(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, 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(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(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, 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(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(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(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(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(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(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(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, 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(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(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, 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(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, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c23_1, c24_1, c25_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, c16_2, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1 ---------------------------------------- (169) 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(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))) ---------------------------------------- (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) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(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)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c18(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c18(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c18(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c18(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c18(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c18(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c18(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c18(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c18(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c18(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(s(z0), x1)) -> c18(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c18(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c18(MARK(recip(z0))) MARK(add(0, x1)) -> c18(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c19(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c19(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c19(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c19(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c19(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c19(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c19(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c19(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c19(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c19(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c19(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c19(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c19(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c19(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c19(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c19(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c19(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c19(MARK(x1)) MARK(add(recip(z0), x1)) -> c19(MARK(x1)) MARK(add(nil, x1)) -> c19(MARK(x1)) MARK(dbl(terms(z0))) -> c20(A__DBL(a__terms(mark(z0))), 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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(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(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(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, 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(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(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, 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(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(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(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(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(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(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(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, 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(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(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, 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(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(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(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)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c18(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c18(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c18(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c18(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c18(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c18(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c18(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c18(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c18(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c18(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(s(z0), x1)) -> c18(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c18(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c18(MARK(recip(z0))) MARK(add(0, x1)) -> c18(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c19(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c19(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c19(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c19(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c19(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c19(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c19(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c19(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c19(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c19(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c19(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c19(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c19(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c19(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c19(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c19(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c19(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c19(MARK(x1)) MARK(add(recip(z0), x1)) -> c19(MARK(x1)) MARK(add(nil, x1)) -> c19(MARK(x1)) MARK(dbl(terms(z0))) -> c20(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c20(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c20(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c20(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c20(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(s(z0))) -> c20(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c20(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c20(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c21(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c21(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c21(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c21(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c21(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c21(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c21(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c21(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c21(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c21(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c21(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(s(z0), x1)) -> c21(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c21(MARK(x0)) MARK(first(x0, s(z0))) -> c21(MARK(x0)) MARK(first(x0, 0)) -> c21(MARK(x0)) MARK(first(x0, nil)) -> c21(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c21(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c21(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c22(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c22(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c22(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c22(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c22(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c22(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c22(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c22(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c22(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c22(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c22(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c22(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c22(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c22(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c22(MARK(x1)) MARK(first(recip(z0), x1)) -> c22(MARK(x1)) MARK(first(0, x1)) -> c22(MARK(x1)) MARK(first(nil, x1)) -> c22(MARK(x1)) 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(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(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, 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(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(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, 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(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__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(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(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(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(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, 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(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(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, 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(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(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(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(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(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(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(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, 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(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(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, 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(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(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(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, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c23_1, c24_1, c25_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, c16_2, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1 ---------------------------------------- (171) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 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) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(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)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c18(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c18(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c18(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c18(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c18(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c18(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c18(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c18(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> 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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(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__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(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(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(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(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, 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(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(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, 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(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(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(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(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(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(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(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, 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(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(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, 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(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(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(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)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c18(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c18(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c18(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c18(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c18(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c18(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c18(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c18(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c18(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c18(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(s(z0), x1)) -> c18(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c18(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c18(MARK(recip(z0))) MARK(add(0, x1)) -> c18(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c19(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c19(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c19(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c19(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c19(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c19(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c19(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c19(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c19(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c19(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c19(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c19(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c19(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c19(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c19(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c19(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c19(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c19(MARK(x1)) MARK(add(recip(z0), x1)) -> c19(MARK(x1)) MARK(add(nil, x1)) -> c19(MARK(x1)) MARK(dbl(terms(z0))) -> c20(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c20(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c20(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c20(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c20(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(s(z0))) -> c20(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c20(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c20(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c21(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c21(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c21(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c21(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c21(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c21(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c21(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c21(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c21(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c21(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c21(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(s(z0), x1)) -> c21(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c21(MARK(x0)) MARK(first(x0, s(z0))) -> c21(MARK(x0)) MARK(first(x0, 0)) -> c21(MARK(x0)) MARK(first(x0, nil)) -> c21(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c21(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c21(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c22(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c22(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c22(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c22(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c22(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c22(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c22(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c22(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c22(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c22(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c22(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c22(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c22(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c22(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c22(MARK(x1)) MARK(first(recip(z0), x1)) -> c22(MARK(x1)) MARK(first(0, x1)) -> c22(MARK(x1)) MARK(first(nil, x1)) -> c22(MARK(x1)) 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(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(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, 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(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(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, 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(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__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(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(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(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(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, 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(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(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, 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(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(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(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(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(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(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(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, 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(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(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, 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(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(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(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, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c23_1, c24_1, c25_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, c16_2, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1 ---------------------------------------- (173) 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(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))) ---------------------------------------- (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) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(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)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), 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MARK(first(terms(z0), x1)) -> c22(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c22(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c22(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c22(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c22(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c22(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c22(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c22(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c22(MARK(x1)) MARK(first(recip(z0), x1)) -> c22(MARK(x1)) MARK(first(0, x1)) -> c22(MARK(x1)) MARK(first(nil, x1)) -> c22(MARK(x1)) 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))) -> 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c(A__SQR(a__add(mark(x0), a__first(mark(z0), mark(z1)))), MARK(add(x0, first(z0, z1)))) 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(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(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, 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(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__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(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(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(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(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, 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(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(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, 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(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(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(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(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(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(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(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, 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(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(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, 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(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(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(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(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)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c18(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c18(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c18(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c18(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c18(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c18(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c18(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c18(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c18(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c18(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(s(z0), x1)) -> c18(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c18(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c18(MARK(recip(z0))) MARK(add(0, x1)) -> c18(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c19(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c19(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c19(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) 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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__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(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(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(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(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, 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(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(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, 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(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(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(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(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(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(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(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, 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(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(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, 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(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(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(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(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, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c23_1, c24_1, c25_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, c16_2, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1 ---------------------------------------- (175) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 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) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(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)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c18(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c18(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c18(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c18(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c18(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c18(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c18(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c18(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c18(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c18(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(s(z0), x1)) -> c18(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c18(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c18(MARK(recip(z0))) MARK(add(0, x1)) -> c18(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c19(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c19(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c19(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c19(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c19(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c19(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c19(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c19(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c19(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c19(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c19(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c19(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c19(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c19(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c19(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c19(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c19(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c19(MARK(x1)) MARK(add(recip(z0), x1)) -> c19(MARK(x1)) MARK(add(nil, x1)) -> c19(MARK(x1)) MARK(dbl(terms(z0))) -> c20(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c20(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c20(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c20(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c20(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(s(z0))) -> c20(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c20(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c20(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c21(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c21(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c21(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c21(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c21(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c21(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c21(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c21(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c21(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c21(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c21(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(s(z0), x1)) -> c21(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c21(MARK(x0)) MARK(first(x0, s(z0))) -> c21(MARK(x0)) MARK(first(x0, 0)) -> c21(MARK(x0)) MARK(first(x0, nil)) -> c21(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c21(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c21(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c22(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c22(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c22(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c22(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c22(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c22(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c22(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c22(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c22(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c22(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c22(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c22(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c22(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c22(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c22(MARK(x1)) MARK(first(recip(z0), x1)) -> c22(MARK(x1)) MARK(first(0, x1)) -> c22(MARK(x1)) MARK(first(nil, x1)) -> c22(MARK(x1)) 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(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(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, 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(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(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, 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(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__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(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(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(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(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, 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(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(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, 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(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(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(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(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(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(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(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, 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(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(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, 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(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(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(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(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)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c18(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c18(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c18(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c18(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c18(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c18(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c18(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c18(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c18(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c18(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(s(z0), x1)) -> c18(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c18(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c18(MARK(recip(z0))) MARK(add(0, x1)) -> c18(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c19(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c19(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c19(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c19(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c19(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c19(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c19(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c19(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c19(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c19(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c19(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c19(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c19(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c19(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c19(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c19(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c19(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c19(MARK(x1)) MARK(add(recip(z0), x1)) -> c19(MARK(x1)) MARK(add(nil, x1)) -> c19(MARK(x1)) MARK(dbl(terms(z0))) -> c20(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c20(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c20(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c20(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c20(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(s(z0))) -> c20(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c20(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c20(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c21(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c21(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c21(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c21(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c21(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c21(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c21(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c21(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c21(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c21(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c21(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(s(z0), x1)) -> c21(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c21(MARK(x0)) MARK(first(x0, s(z0))) -> c21(MARK(x0)) MARK(first(x0, 0)) -> c21(MARK(x0)) MARK(first(x0, nil)) -> c21(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c21(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c21(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c22(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c22(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c22(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c22(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c22(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c22(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c22(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c22(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c22(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c22(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c22(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c22(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c22(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c22(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c22(MARK(x1)) MARK(first(recip(z0), x1)) -> c22(MARK(x1)) MARK(first(0, x1)) -> c22(MARK(x1)) MARK(first(nil, x1)) -> c22(MARK(x1)) 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(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(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, 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(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(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, 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(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__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(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(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(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(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, 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(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(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, 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(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(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(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(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(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(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(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, 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(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(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, 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(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(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(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(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, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c23_1, c24_1, c25_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, c16_2, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1 ---------------------------------------- (177) 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(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))) ---------------------------------------- (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) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(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)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), 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a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c22(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c22(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c22(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c22(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c22(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c22(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c22(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c22(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c22(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c22(MARK(x1)) MARK(first(recip(z0), x1)) -> c22(MARK(x1)) MARK(first(0, x1)) -> c22(MARK(x1)) MARK(first(nil, x1)) -> c22(MARK(x1)) 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(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(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, 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), 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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, 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(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__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(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(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(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(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, 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(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(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, 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(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(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(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(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(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(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(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, 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(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(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, 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(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(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(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(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(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)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c18(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c18(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c18(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c18(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c18(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c18(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c18(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c18(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c18(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c18(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(s(z0), x1)) -> c18(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c18(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c18(MARK(recip(z0))) MARK(add(0, x1)) -> c18(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c19(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c19(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c19(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c19(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c19(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c19(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c19(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c19(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c19(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c19(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c19(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c19(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c19(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c19(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c19(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c19(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c19(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c19(MARK(x1)) MARK(add(recip(z0), x1)) -> c19(MARK(x1)) MARK(add(nil, x1)) -> c19(MARK(x1)) MARK(dbl(terms(z0))) -> c20(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c20(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c20(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c20(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c20(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(s(z0))) -> c20(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c20(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c20(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c21(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c21(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c21(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c21(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c21(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c21(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c21(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c21(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c21(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c21(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c21(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(s(z0), x1)) -> c21(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c21(MARK(x0)) MARK(first(x0, s(z0))) -> c21(MARK(x0)) MARK(first(x0, 0)) -> c21(MARK(x0)) MARK(first(x0, nil)) -> c21(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c21(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c21(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c22(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c22(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c22(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c22(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c22(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c22(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c22(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c22(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c22(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c22(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c22(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c22(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c22(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c22(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c22(MARK(x1)) MARK(first(recip(z0), x1)) -> c22(MARK(x1)) MARK(first(0, x1)) -> c22(MARK(x1)) MARK(first(nil, x1)) -> c22(MARK(x1)) 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(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(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, 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(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(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, 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(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__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(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(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(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(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, 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(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(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, 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(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(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(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(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(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(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(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, 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(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(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, 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(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(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(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(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(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, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c23_1, c24_1, c25_1, c_2, c_1, c3_2, c4_3, c4_2, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c16_2, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c3_3 ---------------------------------------- (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) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(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)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c18(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c18(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c18(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c18(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c18(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c18(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c18(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c18(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c18(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c18(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(s(z0), x1)) -> c18(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c18(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c18(MARK(recip(z0))) MARK(add(0, x1)) -> c18(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c19(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c19(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c19(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c19(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c19(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c19(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c19(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c19(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c19(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c19(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c19(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c19(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c19(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c19(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c19(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c19(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c19(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c19(MARK(x1)) MARK(add(recip(z0), x1)) -> c19(MARK(x1)) MARK(add(nil, x1)) -> c19(MARK(x1)) MARK(dbl(terms(z0))) -> c20(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c20(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c20(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c20(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c20(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(s(z0))) -> c20(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c20(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c20(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c21(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c21(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c21(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c21(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c21(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c21(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c21(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c21(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c21(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c21(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c21(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(s(z0), x1)) -> c21(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c21(MARK(x0)) MARK(first(x0, s(z0))) -> c21(MARK(x0)) MARK(first(x0, 0)) -> c21(MARK(x0)) MARK(first(x0, nil)) -> c21(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c21(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c21(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c22(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c22(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c22(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c22(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c22(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c22(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c22(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c22(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c22(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c22(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c22(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c22(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c22(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c22(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c22(MARK(x1)) MARK(first(recip(z0), x1)) -> c22(MARK(x1)) MARK(first(0, x1)) -> c22(MARK(x1)) MARK(first(nil, x1)) -> c22(MARK(x1)) 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))) -> 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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(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(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, 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(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__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(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(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(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(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, 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(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(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, 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(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(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(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(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(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(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(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, 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(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(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, 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(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(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(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(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(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)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c18(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c18(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c18(A__ADD(mark(x0), 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z1))) -> c19(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c19(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c19(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c19(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c19(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c19(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c19(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c19(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c19(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c19(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c19(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c19(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c19(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c19(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c19(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c19(MARK(x1)) MARK(add(recip(z0), x1)) -> c19(MARK(x1)) MARK(add(nil, x1)) -> c19(MARK(x1)) MARK(dbl(terms(z0))) -> c20(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c20(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c20(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c20(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c20(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(s(z0))) -> c20(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c20(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c20(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c21(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c21(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c21(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c21(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c21(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c21(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c21(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c21(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c21(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c21(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c21(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(s(z0), x1)) -> c21(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c21(MARK(x0)) MARK(first(x0, s(z0))) -> c21(MARK(x0)) MARK(first(x0, 0)) -> c21(MARK(x0)) MARK(first(x0, nil)) -> c21(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c21(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c21(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c22(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c22(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c22(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c22(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c22(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c22(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c22(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c22(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c22(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c22(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c22(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c22(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c22(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c22(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c22(MARK(x1)) MARK(first(recip(z0), x1)) -> c22(MARK(x1)) MARK(first(0, x1)) -> c22(MARK(x1)) MARK(first(nil, x1)) -> c22(MARK(x1)) 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(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(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, 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(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(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, 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(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__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(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(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(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(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, 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(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(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, 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(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(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(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(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(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(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(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, 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(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(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, 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(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(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(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(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(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, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c23_1, c24_1, c25_1, c_2, c_1, c3_2, c4_3, c4_2, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c16_2, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c3_3 ---------------------------------------- (181) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) by A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), 0), A__SQR(mark(0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), dbl(0)), A__SQR(mark(0))) A__SQR(s(0)) -> c3(A__ADD(sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(0)), A__SQR(mark(0))) ---------------------------------------- (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) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(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)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), 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MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c19(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c19(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c19(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c19(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c19(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c19(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c19(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c19(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c19(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c19(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c19(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c19(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c19(MARK(x1)) MARK(add(recip(z0), x1)) -> c19(MARK(x1)) 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MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c21(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c21(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c21(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c21(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c21(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c21(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(s(z0), x1)) -> c21(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c21(MARK(x0)) MARK(first(x0, s(z0))) -> c21(MARK(x0)) MARK(first(x0, 0)) -> c21(MARK(x0)) MARK(first(x0, nil)) -> c21(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c21(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c21(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c22(A__FIRST(mark(x0), a__terms(mark(z0))), 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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, 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(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(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, 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(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__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(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(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(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(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, 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(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(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, 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(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(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(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(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(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(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(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, 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(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(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, 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(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(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(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(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(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))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), 0), A__SQR(mark(0))) A__SQR(s(0)) -> c3(A__ADD(sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(0)), A__SQR(mark(0))) S tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c18(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c18(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c18(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c18(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c18(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c18(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c18(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c18(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c18(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c18(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(s(z0), x1)) -> c18(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c18(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c18(MARK(recip(z0))) MARK(add(0, x1)) -> c18(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c19(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c19(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c19(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) 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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__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(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(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(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(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, 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(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(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, 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(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(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(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(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(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(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(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, 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(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(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, 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(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(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(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(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(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))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), 0), A__SQR(mark(0))) A__SQR(s(0)) -> c3(A__ADD(sqr(mark(0)), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(0)), A__SQR(mark(0))) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c23_1, c24_1, c25_1, c_2, c_1, c3_2, c4_3, c4_2, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c16_2, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c3_3 ---------------------------------------- (183) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 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) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(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)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c18(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c18(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c18(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c18(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c18(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c18(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c18(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c18(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c18(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c18(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(s(z0), x1)) -> c18(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c18(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c18(MARK(recip(z0))) MARK(add(0, x1)) -> c18(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c19(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c19(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c19(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c19(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c19(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c19(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c19(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c19(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c19(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c19(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c19(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c19(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c19(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c19(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c19(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c19(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c19(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c19(MARK(x1)) MARK(add(recip(z0), x1)) -> c19(MARK(x1)) MARK(add(nil, x1)) -> c19(MARK(x1)) MARK(dbl(terms(z0))) -> c20(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c20(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c20(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c20(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c20(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(s(z0))) -> c20(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c20(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c20(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c21(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c21(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c21(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c21(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c21(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c21(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c21(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c21(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c21(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c21(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c21(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(s(z0), x1)) -> c21(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c21(MARK(x0)) MARK(first(x0, s(z0))) -> c21(MARK(x0)) MARK(first(x0, 0)) -> c21(MARK(x0)) MARK(first(x0, nil)) -> c21(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c21(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c21(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c22(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c22(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c22(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c22(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c22(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c22(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c22(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c22(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c22(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c22(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c22(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c22(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c22(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c22(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c22(MARK(x1)) MARK(first(recip(z0), x1)) -> c22(MARK(x1)) MARK(first(0, x1)) -> c22(MARK(x1)) MARK(first(nil, x1)) -> c22(MARK(x1)) 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(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(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, 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(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(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, 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(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__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(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(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(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(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, 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(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(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, 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(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(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(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(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(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(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(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, 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(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(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, 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(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(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(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(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(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))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), 0), A__SQR(mark(0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(0)) -> c3(A__SQR(mark(0))) S tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c18(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c18(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c18(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c18(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c18(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c18(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c18(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c18(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c18(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c18(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(s(z0), x1)) -> c18(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c18(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c18(MARK(recip(z0))) MARK(add(0, x1)) -> c18(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c19(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c19(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c19(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c19(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c19(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c19(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c19(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c19(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c19(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c19(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c19(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c19(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c19(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c19(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c19(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c19(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c19(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c19(MARK(x1)) MARK(add(recip(z0), x1)) -> c19(MARK(x1)) MARK(add(nil, x1)) -> c19(MARK(x1)) MARK(dbl(terms(z0))) -> c20(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c20(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c20(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c20(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c20(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(s(z0))) -> c20(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c20(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c20(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c21(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c21(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c21(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c21(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c21(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c21(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c21(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c21(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c21(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c21(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c21(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(s(z0), x1)) -> c21(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c21(MARK(x0)) MARK(first(x0, s(z0))) -> c21(MARK(x0)) MARK(first(x0, 0)) -> c21(MARK(x0)) MARK(first(x0, nil)) -> c21(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c21(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c21(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c22(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c22(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c22(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c22(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c22(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c22(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c22(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c22(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c22(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c22(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c22(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c22(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c22(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c22(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c22(MARK(x1)) MARK(first(recip(z0), x1)) -> c22(MARK(x1)) MARK(first(0, x1)) -> c22(MARK(x1)) MARK(first(nil, x1)) -> c22(MARK(x1)) 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(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(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, 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(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(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, 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(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__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(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(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(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(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, 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(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(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, 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(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(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(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(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(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(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(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, 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(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(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, 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(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(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(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(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(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))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), 0), A__SQR(mark(0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(0)) -> c3(A__SQR(mark(0))) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c23_1, c24_1, c25_1, c_2, c_1, c3_2, c4_3, c4_2, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c16_2, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c3_3, c3_1 ---------------------------------------- (185) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) by A__SQR(s(nil)) -> c3(A__ADD(a__sqr(mark(nil)), dbl(nil)), A__SQR(mark(nil))) A__SQR(s(nil)) -> c3(A__ADD(sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(nil)), A__SQR(mark(nil))) ---------------------------------------- (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) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(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)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c18(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c18(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c18(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c18(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c18(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c18(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c18(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c18(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c18(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c18(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(s(z0), x1)) -> c18(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c18(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c18(MARK(recip(z0))) MARK(add(0, x1)) -> c18(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c19(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c19(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c19(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c19(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c19(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c19(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c19(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c19(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c19(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c19(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c19(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c19(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c19(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c19(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c19(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c19(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c19(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c19(MARK(x1)) MARK(add(recip(z0), x1)) -> c19(MARK(x1)) MARK(add(nil, x1)) -> c19(MARK(x1)) MARK(dbl(terms(z0))) -> c20(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c20(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c20(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c20(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c20(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(s(z0))) -> c20(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c20(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c20(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c21(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c21(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c21(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c21(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c21(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c21(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c21(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c21(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c21(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c21(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c21(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(s(z0), x1)) -> c21(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c21(MARK(x0)) MARK(first(x0, s(z0))) -> c21(MARK(x0)) MARK(first(x0, 0)) -> c21(MARK(x0)) MARK(first(x0, nil)) -> c21(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c21(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c21(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c22(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c22(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c22(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c22(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c22(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c22(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c22(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c22(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c22(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c22(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c22(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c22(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c22(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c22(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c22(MARK(x1)) MARK(first(recip(z0), x1)) -> c22(MARK(x1)) MARK(first(0, x1)) -> c22(MARK(x1)) MARK(first(nil, x1)) -> c22(MARK(x1)) 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(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(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, 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(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(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, 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(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__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(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(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(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(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, 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(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(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, 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(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(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(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(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(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(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(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, 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(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(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, 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(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(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(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(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(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))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), 0), A__SQR(mark(0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(0)) -> c3(A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(nil)), A__SQR(mark(nil))) S tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c18(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c18(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c18(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c18(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c18(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c18(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c18(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c18(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c18(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c18(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(s(z0), x1)) -> c18(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c18(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c18(MARK(recip(z0))) MARK(add(0, x1)) -> c18(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c19(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c19(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c19(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c19(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c19(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c19(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c19(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c19(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c19(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c19(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c19(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c19(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c19(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c19(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c19(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c19(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c19(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c19(MARK(x1)) MARK(add(recip(z0), x1)) -> c19(MARK(x1)) MARK(add(nil, x1)) -> c19(MARK(x1)) MARK(dbl(terms(z0))) -> c20(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c20(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c20(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c20(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c20(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(s(z0))) -> c20(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c20(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c20(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c21(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c21(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c21(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c21(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c21(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c21(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c21(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c21(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c21(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c21(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c21(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(s(z0), x1)) -> c21(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c21(MARK(x0)) MARK(first(x0, s(z0))) -> c21(MARK(x0)) MARK(first(x0, 0)) -> c21(MARK(x0)) MARK(first(x0, nil)) -> c21(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c21(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c21(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c22(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c22(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c22(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c22(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c22(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c22(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c22(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c22(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c22(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c22(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c22(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c22(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c22(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c22(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c22(MARK(x1)) MARK(first(recip(z0), x1)) -> c22(MARK(x1)) MARK(first(0, x1)) -> c22(MARK(x1)) MARK(first(nil, x1)) -> c22(MARK(x1)) 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(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(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, 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(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(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, 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(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__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(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(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(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(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, 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(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(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, 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(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(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(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(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(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(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(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, 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(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(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, 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(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(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(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(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(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))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), 0), A__SQR(mark(0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(0)) -> c3(A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(sqr(mark(nil)), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(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, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c23_1, c24_1, c25_1, c_2, c_1, c3_2, c4_3, c4_2, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c16_2, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c3_3, c3_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) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(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)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c18(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c18(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c18(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c18(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c18(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c18(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c18(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c18(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c18(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c18(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(s(z0), x1)) -> c18(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c18(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c18(MARK(recip(z0))) MARK(add(0, x1)) -> c18(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c19(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c19(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c19(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c19(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c19(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c19(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c19(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c19(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c19(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c19(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c19(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c19(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c19(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c19(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c19(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c19(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c19(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c19(MARK(x1)) MARK(add(recip(z0), x1)) -> c19(MARK(x1)) MARK(add(nil, x1)) -> c19(MARK(x1)) MARK(dbl(terms(z0))) -> c20(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c20(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c20(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c20(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c20(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(s(z0))) -> c20(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c20(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c20(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c21(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c21(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c21(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c21(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c21(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c21(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c21(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c21(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c21(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c21(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c21(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(s(z0), 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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(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(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, 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(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(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, 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(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(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(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(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(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(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(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, 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(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(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, 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(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(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(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(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(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))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), 0), A__SQR(mark(0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(0)) -> c3(A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(nil)) -> c3(A__SQR(mark(nil))) S tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c18(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c18(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c18(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c18(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c18(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c18(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c18(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c18(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c18(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c18(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(s(z0), x1)) -> c18(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c18(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c18(MARK(recip(z0))) MARK(add(0, x1)) -> c18(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c19(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c19(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c19(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c19(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c19(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c19(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c19(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c19(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c19(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c19(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c19(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c19(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c19(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c19(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c19(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c19(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c19(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c19(MARK(x1)) MARK(add(recip(z0), x1)) -> c19(MARK(x1)) MARK(add(nil, x1)) -> c19(MARK(x1)) MARK(dbl(terms(z0))) -> c20(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c20(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c20(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c20(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c20(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(s(z0))) -> c20(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c20(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c20(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c21(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c21(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c21(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c21(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c21(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c21(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c21(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c21(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c21(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c21(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c21(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(s(z0), x1)) -> c21(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c21(MARK(x0)) MARK(first(x0, s(z0))) -> c21(MARK(x0)) MARK(first(x0, 0)) -> c21(MARK(x0)) MARK(first(x0, nil)) -> c21(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c21(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c21(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c22(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c22(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c22(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c22(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c22(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c22(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c22(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c22(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c22(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c22(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c22(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c22(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c22(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c22(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c22(MARK(x1)) MARK(first(recip(z0), x1)) -> c22(MARK(x1)) MARK(first(0, x1)) -> c22(MARK(x1)) MARK(first(nil, x1)) -> c22(MARK(x1)) 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(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), 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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(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(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, 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(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__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(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(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(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(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, 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(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(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, 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(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(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(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(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(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(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(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, 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(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(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, 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(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(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(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(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(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))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), 0), A__SQR(mark(0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(0)) -> c3(A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(nil)) -> c3(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, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c23_1, c24_1, c25_1, c_2, c_1, c3_2, c4_3, c4_2, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c16_2, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c3_3, c3_1 ---------------------------------------- (189) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__SQR(s(x0)) -> c3(A__SQR(mark(x0)), MARK(x0)) by A__SQR(s(terms(z0))) -> c3(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c3(A__SQR(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__SQR(recip(mark(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__SQR(s(mark(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__SQR(0), MARK(0)) A__SQR(s(nil)) -> c3(A__SQR(nil), MARK(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) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(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)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c18(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c18(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c18(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c18(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c18(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c18(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c18(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c18(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c18(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c18(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(s(z0), x1)) -> c18(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c18(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c18(MARK(recip(z0))) MARK(add(0, x1)) -> c18(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c19(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c19(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c19(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c19(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c19(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c19(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c19(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c19(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c19(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c19(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c19(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c19(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c19(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c19(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c19(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c19(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c19(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c19(MARK(x1)) MARK(add(recip(z0), x1)) -> c19(MARK(x1)) MARK(add(nil, x1)) -> c19(MARK(x1)) MARK(dbl(terms(z0))) -> c20(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c20(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c20(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c20(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c20(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(s(z0))) -> c20(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c20(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c20(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c21(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c21(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c21(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c21(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c21(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c21(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c21(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c21(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c21(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c21(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c21(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(s(z0), x1)) -> c21(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c21(MARK(x0)) MARK(first(x0, s(z0))) -> c21(MARK(x0)) MARK(first(x0, 0)) -> c21(MARK(x0)) MARK(first(x0, nil)) -> c21(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c21(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c21(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c22(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c22(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c22(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c22(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c22(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c22(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c22(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c22(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c22(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c22(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c22(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c22(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c22(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c22(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c22(MARK(x1)) MARK(first(recip(z0), x1)) -> c22(MARK(x1)) MARK(first(0, x1)) -> c22(MARK(x1)) MARK(first(nil, x1)) -> c22(MARK(x1)) 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(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(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, 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(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(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, 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(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__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(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(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(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(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, 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(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(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, 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(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(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(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(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(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(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(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, 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(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(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, 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(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(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(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(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(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))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), 0), A__SQR(mark(0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(0)) -> c3(A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(nil)) -> c3(A__SQR(mark(nil))) A__SQR(s(terms(z0))) -> c3(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c3(A__SQR(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__SQR(recip(mark(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__SQR(s(mark(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__SQR(0), MARK(0)) A__SQR(s(nil)) -> c3(A__SQR(nil), MARK(nil)) S tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), 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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, 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(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(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, 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(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__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(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(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(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(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, 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(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(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, 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(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(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(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(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(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(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(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, 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(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(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, 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(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(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(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(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(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))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), 0), A__SQR(mark(0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(0)) -> c3(A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(nil)) -> c3(A__SQR(mark(nil))) A__SQR(s(terms(z0))) -> c3(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c3(A__SQR(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(A__SQR(recip(mark(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c3(A__SQR(s(mark(z0))), MARK(s(z0))) A__SQR(s(0)) -> c3(A__SQR(0), MARK(0)) A__SQR(s(nil)) -> c3(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, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c23_1, c24_1, c25_1, c_2, c_1, c3_2, c4_3, c4_2, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c16_2, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c3_3, c3_1 ---------------------------------------- (191) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 6 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) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(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)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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__SQR(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), 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MARK(first(terms(z0), x1)) -> c22(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c22(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c22(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c22(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c22(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c22(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c22(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c22(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c22(MARK(x1)) MARK(first(recip(z0), x1)) -> c22(MARK(x1)) MARK(first(0, x1)) -> c22(MARK(x1)) MARK(first(nil, x1)) -> c22(MARK(x1)) 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))) -> 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MARK(first(x0, first(z0, z1)))) 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(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__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(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(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(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(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, 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(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(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, 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(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(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(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(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(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(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(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, 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(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(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, 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(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(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(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(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(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))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), 0), A__SQR(mark(0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(0)) -> c3(A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(nil)) -> c3(A__SQR(mark(nil))) A__SQR(s(terms(z0))) -> c3(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__SQR(s(s(z0))) -> c3(A__SQR(s(mark(z0))), MARK(s(z0))) A__SQR(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(MARK(recip(z0))) A__SQR(s(0)) -> c3 A__SQR(s(nil)) -> c3 S tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(0), a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c18(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c18(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c18(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c18(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c18(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c18(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c18(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c18(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c18(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c18(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(s(z0), x1)) -> c18(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c18(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c18(MARK(recip(z0))) MARK(add(0, x1)) -> c18(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c19(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c19(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c19(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c19(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c19(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c19(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c19(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c19(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c19(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c19(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c19(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c19(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c19(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c19(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c19(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c19(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c19(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c19(MARK(x1)) MARK(add(recip(z0), x1)) -> c19(MARK(x1)) MARK(add(nil, x1)) -> c19(MARK(x1)) MARK(dbl(terms(z0))) -> c20(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c20(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c20(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c20(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c20(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(s(z0))) -> c20(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c20(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c20(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c21(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c21(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c21(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c21(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c21(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c21(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c21(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c21(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c21(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c21(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c21(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(s(z0), x1)) -> c21(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c21(MARK(x0)) MARK(first(x0, s(z0))) -> c21(MARK(x0)) MARK(first(x0, 0)) -> c21(MARK(x0)) MARK(first(x0, nil)) -> c21(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c21(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c21(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c22(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c22(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c22(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c22(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c22(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c22(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c22(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c22(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c22(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c22(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c22(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c22(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c22(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c22(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c22(MARK(x1)) MARK(first(recip(z0), x1)) -> c22(MARK(x1)) MARK(first(0, x1)) -> c22(MARK(x1)) MARK(first(nil, x1)) -> c22(MARK(x1)) 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(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(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, 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(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(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, 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(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__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(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(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(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(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, 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(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(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, 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(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(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(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(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(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(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(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, 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(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(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, 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(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(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(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(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(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))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), 0), A__SQR(mark(0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(0)) -> c3(A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(nil)) -> c3(A__SQR(mark(nil))) A__SQR(s(terms(z0))) -> c3(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__SQR(s(s(z0))) -> c3(A__SQR(s(mark(z0))), MARK(s(z0))) A__SQR(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(MARK(recip(z0))) A__SQR(s(0)) -> c3 A__SQR(s(nil)) -> c3 K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c23_1, c24_1, c25_1, c_2, c_1, c3_2, c4_3, c4_2, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c16_2, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c3_3, c3_1, c3 ---------------------------------------- (193) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) by A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(0)) -> c3(A__ADD(0, a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(0)) -> c3(A__ADD(sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) ---------------------------------------- (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) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(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)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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__SQR(mark(x0)), MARK(x0)) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c18(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c18(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c18(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c18(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c18(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c18(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c18(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c18(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c18(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c18(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(s(z0), x1)) -> c18(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c18(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c18(MARK(recip(z0))) MARK(add(0, x1)) -> c18(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c19(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c19(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c19(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c19(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c19(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c19(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c19(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c19(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c19(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c19(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c19(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c19(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c19(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c19(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c19(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c19(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c19(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c19(MARK(x1)) MARK(add(recip(z0), x1)) -> c19(MARK(x1)) MARK(add(nil, x1)) -> c19(MARK(x1)) MARK(dbl(terms(z0))) -> c20(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c20(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c20(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c20(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c20(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(s(z0))) -> c20(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c20(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c20(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c21(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c21(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c21(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c21(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c21(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c21(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c21(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c21(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c21(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c21(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> 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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(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(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, 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(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(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, 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(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(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(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(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(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(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(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, 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(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(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, 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(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(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(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(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(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))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), 0), A__SQR(mark(0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(0)) -> c3(A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(nil)) -> c3(A__SQR(mark(nil))) A__SQR(s(terms(z0))) -> c3(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__SQR(s(s(z0))) -> c3(A__SQR(s(mark(z0))), MARK(s(z0))) A__SQR(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(MARK(recip(z0))) A__SQR(s(0)) -> c3 A__SQR(s(nil)) -> c3 A__SQR(s(0)) -> c3(A__ADD(0, a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(0)) -> c3(A__ADD(sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) S tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c18(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c18(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c18(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c18(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c18(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c18(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c18(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c18(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c18(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c18(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(s(z0), x1)) -> c18(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c18(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c18(MARK(recip(z0))) MARK(add(0, x1)) -> c18(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c19(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c19(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c19(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c19(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c19(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c19(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c19(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c19(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c19(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c19(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c19(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c19(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c19(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c19(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c19(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c19(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c19(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c19(MARK(x1)) MARK(add(recip(z0), x1)) -> c19(MARK(x1)) MARK(add(nil, x1)) -> c19(MARK(x1)) MARK(dbl(terms(z0))) -> c20(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c20(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c20(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c20(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c20(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(s(z0))) -> c20(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c20(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c20(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c21(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c21(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c21(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c21(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c21(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c21(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c21(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c21(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c21(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c21(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c21(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(s(z0), x1)) -> c21(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c21(MARK(x0)) MARK(first(x0, s(z0))) -> c21(MARK(x0)) MARK(first(x0, 0)) -> c21(MARK(x0)) MARK(first(x0, nil)) -> c21(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c21(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c21(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c22(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c22(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c22(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c22(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c22(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c22(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c22(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c22(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c22(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c22(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c22(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c22(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c22(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c22(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c22(MARK(x1)) MARK(first(recip(z0), x1)) -> c22(MARK(x1)) MARK(first(0, x1)) -> c22(MARK(x1)) MARK(first(nil, x1)) -> c22(MARK(x1)) 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(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(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, 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(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(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, 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(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__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(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(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(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(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, 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(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(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, 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(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(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(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(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(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(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(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, 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(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(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, 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(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(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(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(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(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))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), 0), A__SQR(mark(0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(0)) -> c3(A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(nil)) -> c3(A__SQR(mark(nil))) A__SQR(s(terms(z0))) -> c3(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__SQR(s(s(z0))) -> c3(A__SQR(s(mark(z0))), MARK(s(z0))) A__SQR(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(MARK(recip(z0))) A__SQR(s(0)) -> c3 A__SQR(s(nil)) -> c3 A__SQR(s(0)) -> c3(A__ADD(0, a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(0)) -> c3(A__ADD(sqr(0), a__dbl(mark(0))), A__SQR(mark(0))) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c23_1, c24_1, c25_1, c_2, c_1, c3_2, c4_3, c4_2, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c16_2, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c3_3, c3_1, c3 ---------------------------------------- (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) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(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)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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__SQR(mark(x0)), MARK(x0)) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c18(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c18(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c18(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c18(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c18(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c18(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c18(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c18(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c18(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c18(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(s(z0), x1)) -> c18(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c18(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c18(MARK(recip(z0))) MARK(add(0, x1)) -> c18(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c19(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c19(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c19(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c19(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c19(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c19(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c19(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c19(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c19(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c19(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c19(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c19(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c19(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c19(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c19(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c19(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c19(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c19(MARK(x1)) MARK(add(recip(z0), x1)) -> c19(MARK(x1)) MARK(add(nil, x1)) -> c19(MARK(x1)) MARK(dbl(terms(z0))) -> c20(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c20(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c20(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c20(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c20(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(s(z0))) -> c20(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c20(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c20(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c21(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c21(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c21(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c21(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c21(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c21(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c21(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c21(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c21(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c21(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c21(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(s(z0), x1)) -> c21(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c21(MARK(x0)) MARK(first(x0, s(z0))) -> c21(MARK(x0)) MARK(first(x0, 0)) -> c21(MARK(x0)) MARK(first(x0, nil)) -> c21(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c21(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c21(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c22(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c22(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c22(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c22(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c22(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c22(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c22(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c22(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c22(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c22(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c22(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c22(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c22(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c22(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c22(MARK(x1)) MARK(first(recip(z0), x1)) -> c22(MARK(x1)) MARK(first(0, x1)) -> c22(MARK(x1)) MARK(first(nil, x1)) -> c22(MARK(x1)) 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(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), 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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(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(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, 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(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__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(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(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(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(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, 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(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(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, 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(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(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(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(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(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(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(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, 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(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(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, 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(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(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(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(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(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))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), 0), A__SQR(mark(0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(0)) -> c3(A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(nil)) -> c3(A__SQR(mark(nil))) A__SQR(s(terms(z0))) -> c3(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__SQR(s(s(z0))) -> c3(A__SQR(s(mark(z0))), MARK(s(z0))) A__SQR(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(MARK(recip(z0))) A__SQR(s(0)) -> c3 A__SQR(s(nil)) -> c3 A__SQR(s(0)) -> c3(A__ADD(0, a__dbl(mark(0))), A__SQR(mark(0))) S tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c18(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c18(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c18(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c18(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c18(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c18(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c18(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c18(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c18(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c18(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(s(z0), x1)) -> c18(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c18(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c18(MARK(recip(z0))) MARK(add(0, x1)) -> c18(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c19(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c19(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c19(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c19(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c19(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c19(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c19(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c19(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c19(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c19(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c19(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c19(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c19(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c19(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c19(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c19(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c19(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c19(MARK(x1)) MARK(add(recip(z0), x1)) -> c19(MARK(x1)) MARK(add(nil, x1)) -> c19(MARK(x1)) MARK(dbl(terms(z0))) -> c20(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c20(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c20(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c20(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c20(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(s(z0))) -> c20(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c20(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c20(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c21(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c21(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c21(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c21(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c21(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c21(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c21(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c21(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c21(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c21(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c21(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(s(z0), x1)) -> c21(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c21(MARK(x0)) MARK(first(x0, s(z0))) -> c21(MARK(x0)) MARK(first(x0, 0)) -> c21(MARK(x0)) MARK(first(x0, nil)) -> c21(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c21(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c21(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c22(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c22(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c22(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c22(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c22(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c22(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c22(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c22(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c22(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c22(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c22(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c22(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c22(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c22(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c22(MARK(x1)) MARK(first(recip(z0), x1)) -> c22(MARK(x1)) MARK(first(0, x1)) -> c22(MARK(x1)) MARK(first(nil, x1)) -> c22(MARK(x1)) 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(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(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, 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(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(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, 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(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__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(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(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(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(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, 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(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(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, 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(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(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(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(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(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(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(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, 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(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(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, 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(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(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(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(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(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))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), 0), A__SQR(mark(0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(0)) -> c3(A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(nil)) -> c3(A__SQR(mark(nil))) A__SQR(s(terms(z0))) -> c3(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__SQR(s(s(z0))) -> c3(A__SQR(s(mark(z0))), MARK(s(z0))) A__SQR(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(MARK(recip(z0))) A__SQR(s(0)) -> c3 A__SQR(s(nil)) -> c3 A__SQR(s(0)) -> c3(A__ADD(0, a__dbl(mark(0))), A__SQR(mark(0))) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c23_1, c24_1, c25_1, c_2, c_1, c3_2, c4_3, c4_2, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c16_2, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c3_3, c3_1, c3 ---------------------------------------- (197) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__SQR(mark(nil))) by A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), dbl(mark(nil))), A__SQR(mark(nil))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(nil)) -> c3(A__ADD(sqr(nil), a__dbl(mark(nil))), A__SQR(mark(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) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(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)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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__SQR(mark(x0)), MARK(x0)) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), 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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, 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(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(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, 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(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__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(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(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(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(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, 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(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(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, 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(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(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(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(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(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(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(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, 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(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(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, 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(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(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(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(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(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))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), 0), A__SQR(mark(0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(0)) -> c3(A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(nil)) -> c3(A__SQR(mark(nil))) A__SQR(s(terms(z0))) -> c3(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__SQR(s(s(z0))) -> c3(A__SQR(s(mark(z0))), MARK(s(z0))) A__SQR(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(MARK(recip(z0))) A__SQR(s(0)) -> c3 A__SQR(s(nil)) -> c3 A__SQR(s(0)) -> c3(A__ADD(0, a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(sqr(nil), a__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)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c18(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c18(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c18(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c18(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c18(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c18(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c18(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c18(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c18(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c18(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(s(z0), x1)) -> c18(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c18(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c18(MARK(recip(z0))) MARK(add(0, x1)) -> c18(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c19(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c19(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c19(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c19(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c19(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c19(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c19(A__ADD(mark(x0), recip(mark(z0))), 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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(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(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(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(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, 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(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(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, 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(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(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(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(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(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(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(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, 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(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(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, 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(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(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(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(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(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))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), 0), A__SQR(mark(0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(0)) -> c3(A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(nil)) -> c3(A__SQR(mark(nil))) A__SQR(s(terms(z0))) -> c3(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__SQR(s(s(z0))) -> c3(A__SQR(s(mark(z0))), MARK(s(z0))) A__SQR(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(MARK(recip(z0))) A__SQR(s(0)) -> c3 A__SQR(s(nil)) -> c3 A__SQR(s(0)) -> c3(A__ADD(0, a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(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, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c23_1, c24_1, c25_1, c_2, c_1, c3_2, c4_3, c4_2, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c16_2, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c3_3, c3_1, c3 ---------------------------------------- (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) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(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)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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__SQR(mark(x0)), MARK(x0)) A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c18(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c18(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c18(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c18(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c18(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c18(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c18(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c18(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c18(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c18(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(s(z0), x1)) -> c18(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c18(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c18(MARK(recip(z0))) MARK(add(0, x1)) -> c18(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c19(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c19(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c19(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c19(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c19(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c19(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c19(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c19(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c19(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c19(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c19(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c19(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c19(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c19(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c19(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c19(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c19(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c19(MARK(x1)) MARK(add(recip(z0), x1)) -> c19(MARK(x1)) MARK(add(nil, x1)) -> c19(MARK(x1)) MARK(dbl(terms(z0))) -> c20(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c20(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c20(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c20(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c20(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(s(z0))) -> c20(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c20(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c20(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c21(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c21(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c21(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c21(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c21(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), 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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(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__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(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))) 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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(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(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, 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(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(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, 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(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(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(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(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(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(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(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, 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(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(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, 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(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(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(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(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(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))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), 0), A__SQR(mark(0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(0)) -> c3(A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(nil)) -> c3(A__SQR(mark(nil))) A__SQR(s(terms(z0))) -> c3(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__SQR(s(s(z0))) -> c3(A__SQR(s(mark(z0))), MARK(s(z0))) A__SQR(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(MARK(recip(z0))) A__SQR(s(0)) -> c3 A__SQR(s(nil)) -> c3 A__SQR(s(0)) -> c3(A__ADD(0, a__dbl(mark(0))), A__SQR(mark(0))) S tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c18(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c18(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c18(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c18(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c18(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c18(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c18(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c18(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c18(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c18(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(s(z0), x1)) -> c18(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c18(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c18(MARK(recip(z0))) MARK(add(0, x1)) -> c18(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c19(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c19(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c19(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c19(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c19(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c19(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c19(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c19(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c19(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c19(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c19(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c19(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c19(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c19(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c19(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c19(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c19(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c19(MARK(x1)) MARK(add(recip(z0), x1)) -> c19(MARK(x1)) MARK(add(nil, x1)) -> c19(MARK(x1)) MARK(dbl(terms(z0))) -> c20(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c20(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c20(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c20(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c20(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(s(z0))) -> c20(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c20(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c20(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c21(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c21(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c21(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c21(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c21(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c21(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c21(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c21(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c21(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c21(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c21(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(s(z0), x1)) -> c21(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c21(MARK(x0)) MARK(first(x0, s(z0))) -> c21(MARK(x0)) MARK(first(x0, 0)) -> c21(MARK(x0)) MARK(first(x0, nil)) -> c21(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c21(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c21(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c22(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c22(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c22(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c22(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c22(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c22(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c22(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c22(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c22(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c22(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c22(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c22(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c22(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c22(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c22(MARK(x1)) MARK(first(recip(z0), x1)) -> c22(MARK(x1)) MARK(first(0, x1)) -> c22(MARK(x1)) MARK(first(nil, x1)) -> c22(MARK(x1)) 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(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(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, 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(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(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, 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(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__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(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(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(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(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, 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(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(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, 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(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(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(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(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(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(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(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, 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(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(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, 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(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(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(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(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(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))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), 0), A__SQR(mark(0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(0)) -> c3(A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(nil)) -> c3(A__SQR(mark(nil))) A__SQR(s(terms(z0))) -> c3(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__SQR(s(s(z0))) -> c3(A__SQR(s(mark(z0))), MARK(s(z0))) A__SQR(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(MARK(recip(z0))) A__SQR(s(0)) -> c3 A__SQR(s(nil)) -> c3 A__SQR(s(0)) -> c3(A__ADD(0, a__dbl(mark(0))), A__SQR(mark(0))) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c23_1, c24_1, c25_1, c_2, c_1, c3_2, c4_3, c4_2, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c16_2, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c3_3, c3_1, c3 ---------------------------------------- (201) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__SQR(s(x0)) -> c4(A__ADD(a__sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) by A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), dbl(0)), A__DBL(mark(0)), MARK(0)) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), dbl(nil)), A__DBL(mark(nil)), MARK(nil)) A__SQR(s(x0)) -> c4(A__ADD(sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), dbl(mark(0))), A__DBL(mark(0)), MARK(0)) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), dbl(mark(nil))), A__DBL(mark(nil)), MARK(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) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(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)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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__SQR(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c18(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c18(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c18(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c18(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c18(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c18(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c18(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c18(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c18(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c18(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(s(z0), x1)) -> c18(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c18(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c18(MARK(recip(z0))) MARK(add(0, x1)) -> c18(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c19(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c19(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c19(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c19(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c19(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c19(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c19(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c19(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c19(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c19(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c19(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c19(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c19(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c19(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c19(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c19(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c19(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c19(MARK(x1)) MARK(add(recip(z0), x1)) -> c19(MARK(x1)) MARK(add(nil, x1)) -> c19(MARK(x1)) MARK(dbl(terms(z0))) -> c20(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c20(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c20(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c20(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c20(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(s(z0))) -> c20(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c20(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c20(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c21(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c21(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c21(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c21(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c21(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c21(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c21(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c21(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c21(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c21(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c21(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(s(z0), x1)) -> c21(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c21(MARK(x0)) MARK(first(x0, s(z0))) -> c21(MARK(x0)) MARK(first(x0, 0)) -> c21(MARK(x0)) MARK(first(x0, nil)) -> c21(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c21(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c21(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c22(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c22(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c22(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c22(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c22(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c22(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c22(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c22(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c22(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c22(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c22(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c22(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c22(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c22(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c22(MARK(x1)) MARK(first(recip(z0), x1)) -> c22(MARK(x1)) MARK(first(0, x1)) -> c22(MARK(x1)) MARK(first(nil, x1)) -> c22(MARK(x1)) 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(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(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, 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(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(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, 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(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__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(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(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(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(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, 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(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(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, 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(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(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(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(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(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(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(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, 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(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(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, 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(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(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(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(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(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))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), 0), A__SQR(mark(0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(0)) -> c3(A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(nil)) -> c3(A__SQR(mark(nil))) A__SQR(s(terms(z0))) -> c3(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__SQR(s(s(z0))) -> c3(A__SQR(s(mark(z0))), MARK(s(z0))) A__SQR(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(MARK(recip(z0))) A__SQR(s(0)) -> c3 A__SQR(s(nil)) -> c3 A__SQR(s(0)) -> c3(A__ADD(0, a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), dbl(0)), A__DBL(mark(0)), MARK(0)) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), dbl(nil)), A__DBL(mark(nil)), MARK(nil)) A__SQR(s(x0)) -> c4(A__ADD(sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), dbl(mark(0))), A__DBL(mark(0)), MARK(0)) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), dbl(mark(nil))), A__DBL(mark(nil)), MARK(nil)) S tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c18(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c18(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c18(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c18(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c18(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c18(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c18(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c18(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c18(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c18(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(s(z0), x1)) -> c18(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c18(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c18(MARK(recip(z0))) MARK(add(0, x1)) -> c18(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c19(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c19(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c19(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c19(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c19(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c19(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c19(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c19(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c19(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c19(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c19(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c19(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c19(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c19(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c19(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c19(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c19(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c19(MARK(x1)) MARK(add(recip(z0), x1)) -> c19(MARK(x1)) MARK(add(nil, x1)) -> c19(MARK(x1)) MARK(dbl(terms(z0))) -> c20(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c20(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c20(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c20(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c20(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(s(z0))) -> c20(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c20(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c20(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c21(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c21(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c21(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c21(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c21(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c21(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c21(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c21(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c21(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c21(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c21(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(s(z0), x1)) -> c21(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c21(MARK(x0)) MARK(first(x0, s(z0))) -> c21(MARK(x0)) MARK(first(x0, 0)) -> c21(MARK(x0)) MARK(first(x0, nil)) -> c21(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c21(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c21(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c22(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c22(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c22(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c22(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c22(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c22(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c22(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c22(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c22(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c22(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c22(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c22(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c22(MARK(recip(z0))) MARK(first(x0, s(z0))) -> c22(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c22(MARK(x1)) MARK(first(recip(z0), x1)) -> c22(MARK(x1)) MARK(first(0, x1)) -> c22(MARK(x1)) MARK(first(nil, x1)) -> c22(MARK(x1)) 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(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(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, 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(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(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, 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(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__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(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(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(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(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, 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(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(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, 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(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(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(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(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(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(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(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, 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(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(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, 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(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(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(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(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(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))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), 0), A__SQR(mark(0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(0)) -> c3(A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(nil)) -> c3(A__SQR(mark(nil))) A__SQR(s(terms(z0))) -> c3(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__SQR(s(s(z0))) -> c3(A__SQR(s(mark(z0))), MARK(s(z0))) A__SQR(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(MARK(recip(z0))) A__SQR(s(0)) -> c3 A__SQR(s(nil)) -> c3 A__SQR(s(0)) -> c3(A__ADD(0, a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), dbl(0)), A__DBL(mark(0)), MARK(0)) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), dbl(nil)), A__DBL(mark(nil)), MARK(nil)) A__SQR(s(x0)) -> c4(A__ADD(sqr(mark(x0)), dbl(mark(x0))), A__DBL(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), dbl(mark(0))), A__DBL(mark(0)), MARK(0)) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), 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, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c23_1, c24_1, c25_1, c_2, c_1, c3_2, c4_3, c4_2, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c16_2, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c3_3, c3_1, c3 ---------------------------------------- (203) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 5 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) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(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)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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__SQR(mark(x0)), MARK(x0)) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c18(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c18(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c18(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c18(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c18(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c18(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c18(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c18(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c18(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c18(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(s(z0), x1)) -> c18(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c18(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c18(MARK(recip(z0))) MARK(add(0, x1)) -> c18(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c19(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c19(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c19(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c19(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c19(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c19(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c19(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c19(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c19(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c19(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c19(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c19(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c19(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c19(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c19(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c19(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c19(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c19(MARK(x1)) MARK(add(recip(z0), x1)) -> c19(MARK(x1)) MARK(add(nil, x1)) -> c19(MARK(x1)) MARK(dbl(terms(z0))) -> c20(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c20(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c20(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c20(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c20(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(s(z0))) -> c20(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c20(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c20(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c21(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c21(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c21(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c21(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c21(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c21(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c21(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c21(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c21(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c21(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c21(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(s(z0), x1)) -> c21(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c21(MARK(x0)) MARK(first(x0, s(z0))) -> c21(MARK(x0)) MARK(first(x0, 0)) -> c21(MARK(x0)) MARK(first(x0, nil)) -> c21(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c21(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c21(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c22(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c22(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c22(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c22(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c22(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c22(A__FIRST(mark(x0), cons(mark(z0), z1)), 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-> 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(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(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, 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), 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c(A__SQR(a__dbl(a__first(mark(z0), mark(z1)))), MARK(dbl(first(z0, z1)))) 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, 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(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__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(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(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(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(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, 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(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(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, 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(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(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(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(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(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(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(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, 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(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(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, 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(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(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(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(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(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))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), 0), A__SQR(mark(0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(0)) -> c3(A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(nil)) -> c3(A__SQR(mark(nil))) A__SQR(s(terms(z0))) -> c3(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__SQR(s(s(z0))) -> c3(A__SQR(s(mark(z0))), MARK(s(z0))) A__SQR(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(MARK(recip(z0))) A__SQR(s(0)) -> c3 A__SQR(s(nil)) -> c3 A__SQR(s(0)) -> c3(A__ADD(0, a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), dbl(nil)), A__DBL(mark(nil))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), dbl(mark(nil))), A__DBL(mark(nil))) S tuples: A__ADD(0, z0) -> c9(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c14(MARK(z1)) MARK(cons(z0, z1)) -> c23(MARK(z0)) MARK(recip(z0)) -> c24(MARK(z0)) MARK(s(z0)) -> c25(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))) -> c4(A__ADD(a__sqr(mark(terms(z0))), a__dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), a__dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), a__dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), a__dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), a__dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), a__dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), a__dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), a__dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), a__dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), a__dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), a__dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), a__dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), a__dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), a__dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), a__dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), a__dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), a__dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), a__dbl(nil)), A__DBL(mark(nil))) A__SQR(s(x0)) -> c4(A__DBL(mark(x0)), MARK(x0)) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), a__dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), a__dbl(mark(nil))), A__DBL(mark(nil))) A__DBL(s(terms(z0))) -> c7(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) A__DBL(s(sqr(z0))) -> c7(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) A__DBL(s(add(z0, z1))) -> c7(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__DBL(s(dbl(z0))) -> c7(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) A__DBL(s(first(z0, z1))) -> c7(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__DBL(s(s(z0))) -> c7(A__DBL(s(mark(z0))), MARK(s(z0))) A__DBL(s(cons(z0, z1))) -> c7(MARK(cons(z0, z1))) A__DBL(s(recip(z0))) -> c7(MARK(recip(z0))) A__ADD(s(x0), terms(z0)) -> c10(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) A__ADD(s(x0), sqr(z0)) -> c10(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) A__ADD(s(x0), add(z0, z1)) -> c10(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), dbl(z0)) -> c10(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) A__ADD(s(x0), first(z0, z1)) -> c10(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) A__ADD(s(x0), cons(z0, z1)) -> c10(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__ADD(s(x0), recip(z0)) -> c10(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) A__ADD(s(x0), s(z0)) -> c10(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) A__ADD(s(x0), 0) -> c10(A__ADD(mark(x0), 0), MARK(x0)) A__ADD(s(x0), nil) -> c10(A__ADD(mark(x0), nil), MARK(x0)) A__ADD(s(terms(z0)), x1) -> c10(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) A__ADD(s(sqr(z0)), x1) -> c10(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) A__ADD(s(add(z0, z1)), x1) -> c10(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) A__ADD(s(dbl(z0)), x1) -> c10(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) A__ADD(s(first(z0, z1)), x1) -> c10(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) A__ADD(s(s(z0)), x1) -> c10(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) A__ADD(s(cons(z0, z1)), x1) -> c10(MARK(cons(z0, z1))) A__ADD(s(recip(z0)), x1) -> c10(MARK(recip(z0))) A__ADD(s(0), x1) -> c10(A__ADD(0, mark(x1))) A__ADD(s(x0), terms(z0)) -> c11(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) A__ADD(s(x0), sqr(z0)) -> c11(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) A__ADD(s(x0), add(z0, z1)) -> c11(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__ADD(s(x0), dbl(z0)) -> c11(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) A__ADD(s(x0), first(z0, z1)) -> c11(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__ADD(s(x0), cons(z0, z1)) -> c11(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__ADD(s(x0), recip(z0)) -> c11(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) A__ADD(s(x0), s(z0)) -> c11(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) A__ADD(s(terms(z0)), x1) -> c11(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(sqr(z0)), x1) -> c11(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(add(z0, z1)), x1) -> c11(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(dbl(z0)), x1) -> c11(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(first(z0, z1)), x1) -> c11(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__ADD(s(s(z0)), x1) -> c11(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) A__ADD(s(0), x1) -> c11(A__ADD(0, mark(x1)), MARK(x1)) A__ADD(s(x0), 0) -> c11(A__ADD(mark(x0), 0)) A__ADD(s(x0), nil) -> c11(A__ADD(mark(x0), nil)) A__ADD(s(cons(z0, z1)), x1) -> c11(MARK(x1)) A__ADD(s(recip(z0)), x1) -> c11(MARK(x1)) A__ADD(s(nil), x1) -> c11(MARK(x1)) MARK(terms(terms(z0))) -> c16(A__TERMS(a__terms(mark(z0))), MARK(terms(z0))) MARK(terms(sqr(z0))) -> c16(A__TERMS(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(terms(add(z0, z1))) -> c16(A__TERMS(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(terms(dbl(z0))) -> c16(A__TERMS(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(terms(first(z0, z1))) -> c16(A__TERMS(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(terms(cons(z0, z1))) -> c16(A__TERMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(terms(recip(z0))) -> c16(A__TERMS(recip(mark(z0))), MARK(recip(z0))) MARK(terms(s(z0))) -> c16(A__TERMS(s(mark(z0))), MARK(s(z0))) MARK(sqr(terms(z0))) -> c17(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) MARK(sqr(sqr(z0))) -> c17(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(sqr(add(z0, z1))) -> c17(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(sqr(dbl(z0))) -> c17(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(sqr(first(z0, z1))) -> c17(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sqr(s(z0))) -> c17(A__SQR(s(mark(z0))), MARK(s(z0))) MARK(sqr(cons(z0, z1))) -> c17(MARK(cons(z0, z1))) MARK(sqr(recip(z0))) -> c17(MARK(recip(z0))) MARK(add(x0, terms(z0))) -> c18(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c18(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c18(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c18(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c18(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c18(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c18(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c18(A__ADD(mark(x0), s(mark(z0))), MARK(x0)) MARK(add(x0, 0)) -> c18(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c18(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c18(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c18(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c18(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c18(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c18(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(s(z0), x1)) -> c18(A__ADD(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(add(cons(z0, z1), x1)) -> c18(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c18(MARK(recip(z0))) MARK(add(0, x1)) -> c18(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c19(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c19(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c19(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c19(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c19(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c19(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c19(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c19(A__ADD(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(add(terms(z0), x1)) -> c19(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c19(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c19(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c19(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c19(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c19(A__ADD(s(mark(z0)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c19(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c19(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c19(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c19(MARK(x1)) MARK(add(recip(z0), x1)) -> c19(MARK(x1)) MARK(add(nil, x1)) -> c19(MARK(x1)) MARK(dbl(terms(z0))) -> c20(A__DBL(a__terms(mark(z0))), MARK(terms(z0))) MARK(dbl(sqr(z0))) -> c20(A__DBL(a__sqr(mark(z0))), MARK(sqr(z0))) MARK(dbl(add(z0, z1))) -> c20(A__DBL(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(dbl(dbl(z0))) -> c20(A__DBL(a__dbl(mark(z0))), MARK(dbl(z0))) MARK(dbl(first(z0, z1))) -> c20(A__DBL(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(dbl(s(z0))) -> c20(A__DBL(s(mark(z0))), MARK(s(z0))) MARK(dbl(cons(z0, z1))) -> c20(MARK(cons(z0, z1))) MARK(dbl(recip(z0))) -> c20(MARK(recip(z0))) MARK(first(x0, terms(z0))) -> c21(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c21(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c21(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c21(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c21(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c21(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c21(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c21(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c21(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c21(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c21(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(s(z0), x1)) -> c21(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, recip(z0))) -> c21(MARK(x0)) MARK(first(x0, s(z0))) -> c21(MARK(x0)) MARK(first(x0, 0)) -> 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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__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(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))), 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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(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(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, 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(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(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, 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(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(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(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(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(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(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(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, 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(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(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, 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(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(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(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(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(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))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(mark(0)), 0), A__SQR(mark(0))) A__SQR(s(0)) -> c3(A__ADD(a__sqr(0), a__dbl(0)), A__SQR(mark(0))) A__SQR(s(0)) -> c3(A__SQR(mark(0))) A__SQR(s(nil)) -> c3(A__ADD(a__sqr(nil), a__dbl(nil)), A__SQR(mark(nil))) A__SQR(s(nil)) -> c3(A__SQR(mark(nil))) A__SQR(s(terms(z0))) -> c3(A__SQR(a__terms(mark(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c3(A__SQR(a__sqr(mark(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c3(A__SQR(a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c3(A__SQR(a__dbl(mark(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c3(A__SQR(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__SQR(s(s(z0))) -> c3(A__SQR(s(mark(z0))), MARK(s(z0))) A__SQR(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c3(MARK(recip(z0))) A__SQR(s(0)) -> c3 A__SQR(s(nil)) -> c3 A__SQR(s(0)) -> c3(A__ADD(0, a__dbl(mark(0))), A__SQR(mark(0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(mark(terms(z0))), dbl(a__terms(mark(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(mark(sqr(z0))), dbl(a__sqr(mark(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(mark(add(z0, z1))), dbl(a__add(mark(z0), mark(z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(mark(dbl(z0))), dbl(a__dbl(mark(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(mark(first(z0, z1))), dbl(a__first(mark(z0), mark(z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(mark(cons(z0, z1))), dbl(cons(mark(z0), z1))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(mark(recip(z0))), dbl(recip(mark(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(mark(s(z0))), dbl(s(mark(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(terms(z0))) -> c4(A__ADD(a__sqr(a__terms(mark(z0))), dbl(mark(terms(z0)))), A__DBL(mark(terms(z0))), MARK(terms(z0))) A__SQR(s(sqr(z0))) -> c4(A__ADD(a__sqr(a__sqr(mark(z0))), dbl(mark(sqr(z0)))), A__DBL(mark(sqr(z0))), MARK(sqr(z0))) A__SQR(s(add(z0, z1))) -> c4(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), dbl(mark(add(z0, z1)))), A__DBL(mark(add(z0, z1))), MARK(add(z0, z1))) A__SQR(s(dbl(z0))) -> c4(A__ADD(a__sqr(a__dbl(mark(z0))), dbl(mark(dbl(z0)))), A__DBL(mark(dbl(z0))), MARK(dbl(z0))) A__SQR(s(first(z0, z1))) -> c4(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), dbl(mark(first(z0, z1)))), A__DBL(mark(first(z0, z1))), MARK(first(z0, z1))) A__SQR(s(cons(z0, z1))) -> c4(A__ADD(a__sqr(cons(mark(z0), z1)), dbl(mark(cons(z0, z1)))), A__DBL(mark(cons(z0, z1))), MARK(cons(z0, z1))) A__SQR(s(recip(z0))) -> c4(A__ADD(a__sqr(recip(mark(z0))), dbl(mark(recip(z0)))), A__DBL(mark(recip(z0))), MARK(recip(z0))) A__SQR(s(s(z0))) -> c4(A__ADD(a__sqr(s(mark(z0))), dbl(mark(s(z0)))), A__DBL(mark(s(z0))), MARK(s(z0))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(mark(0)), dbl(0)), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(mark(nil)), dbl(nil)), A__DBL(mark(nil))) A__SQR(s(0)) -> c4(A__ADD(a__sqr(0), dbl(mark(0))), A__DBL(mark(0))) A__SQR(s(nil)) -> c4(A__ADD(a__sqr(nil), 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, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1, A__SQR_1, A__DBL_1 Compound Symbols: c9_1, c14_1, c23_1, c24_1, c25_1, c_2, c_1, c3_2, c4_3, c4_2, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c16_2, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c3_3, c3_1, c3