KILLED proof of input_pTbKa17CMA.trs # AProVE Commit ID: aff8ecad908e01718a4c36e68d2e55d5e0f16e15 fuhs 20220216 unpublished The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF).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), 0 ms] (12) CpxTypedWeightedCompleteTrs (13) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 11 ms] (14) CpxRNTS (15) InliningProof [UPPER BOUND(ID), 282 ms] (16) CpxRNTS (17) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] (18) CpxRNTS (19) CompletionProof [UPPER BOUND(ID), 0 ms] (20) CpxTypedWeightedCompleteTrs (21) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 14 ms] (22) CpxRNTS (23) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] (24) CdtProblem (25) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms] (26) CdtProblem (27) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (28) CdtProblem (29) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms] (30) CdtProblem (31) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 188 ms] (32) CdtProblem (33) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (34) CdtProblem (35) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (36) CdtProblem (37) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (38) CdtProblem (39) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (40) CdtProblem (41) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (42) CdtProblem (43) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (44) CdtProblem (45) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (46) CdtProblem (47) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (48) CdtProblem (49) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (50) CdtProblem (51) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (52) CdtProblem (53) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (54) CdtProblem (55) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (56) CdtProblem (57) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (58) CdtProblem (59) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (60) CdtProblem (61) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 5 ms] (62) CdtProblem (63) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (64) CdtProblem (65) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (66) CdtProblem (67) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (68) CdtProblem (69) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms] (70) CdtProblem (71) CdtRewritingProof [BOTH BOUNDS(ID, ID), 1 ms] (72) CdtProblem (73) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (74) CdtProblem (75) CdtInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (76) CdtProblem (77) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 137 ms] (78) CdtProblem (79) CdtInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (80) CdtProblem (81) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms] (82) CdtProblem (83) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 116 ms] (84) CdtProblem (85) CdtInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (86) CdtProblem (87) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms] (88) CdtProblem (89) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 124 ms] (90) CdtProblem (91) CdtInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (92) CdtProblem (93) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 144 ms] (94) CdtProblem (95) CdtInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (96) CdtProblem (97) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms] (98) CdtProblem (99) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 140 ms] (100) CdtProblem (101) CdtInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (102) CdtProblem (103) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 138 ms] (104) CdtProblem (105) CdtInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (106) CdtProblem (107) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms] (108) CdtProblem (109) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 175 ms] (110) CdtProblem (111) CdtInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (112) CdtProblem (113) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms] (114) CdtProblem (115) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 184 ms] (116) CdtProblem (117) CdtInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (118) CdtProblem (119) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms] (120) CdtProblem (121) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 186 ms] (122) CdtProblem (123) CdtInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (124) CdtProblem (125) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 193 ms] (126) CdtProblem (127) CdtInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (128) CdtProblem (129) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 179 ms] (130) CdtProblem (131) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (132) CdtProblem (133) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (134) CdtProblem (135) CdtRewritingProof [BOTH BOUNDS(ID, ID), 22 ms] (136) CdtProblem (137) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (138) CdtProblem (139) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (140) CdtProblem (141) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (142) CdtProblem (143) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (144) CdtProblem (145) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (146) CdtProblem (147) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (148) CdtProblem (149) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (150) CdtProblem (151) CdtRewritingProof [BOTH BOUNDS(ID, ID), 8 ms] (152) CdtProblem (153) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms] (154) CdtProblem (155) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (156) CdtProblem (157) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (158) CdtProblem (159) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (160) 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: fibs_2#1(zipwith_l, plus, tail_l, x3) -> ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))) cond_take_l_n_xs(ConsL(x16, x18), 0) -> Nil cond_take_l_n_xs(ConsL(x7, fibs_2(x4, x8, x12)), S(x16)) -> Cons(x7, cond_take_l_n_xs(fibs_2#1(x4, x8, x12, bot[0]), x16)) cond_take_l_n_xs(ConsL(x7, zipwith_l_f_xs_ys(x4, x8, x12)), S(x16)) -> Cons(x7, cond_take_l_n_xs(zipwith_l_f_xs_ys#1(x4, x8, x12, bot[0]), x16)) plus#2(0, x12) -> x12 plus#2(S(x4), x2) -> S(plus#2(x4, x2)) cond_zipwith_l_f_xs_ys_1(ConsL(x4, x3), x2, x1) -> ConsL(plus#2(x2, x4), zipwith_l#3(x1, x3)) cond_zipwith_l_f_xs_ys(ConsL(x5, x4), zipwith_l_f_xs_ys(x1, x2, x3)) -> cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(x1, x2, x3, bot[6]), x5, x4) cond_zipwith_l_f_xs_ys(ConsL(x5, x4), fibs_2(x1, x2, x3)) -> cond_zipwith_l_f_xs_ys_1(fibs_2#1(x1, x2, x3, bot[6]), x5, x4) zipwith_l_f_xs_ys#1(plus, fibs, x5, x3) -> cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x5) zipwith_l_f_xs_ys#1(plus, fibs_2(x3, x4, x5), x2, x1) -> cond_zipwith_l_f_xs_ys(fibs_2#1(x3, x4, x5, bot[7]), x2) zipwith_l_f_xs_ys#1(plus, zipwith_l_f_xs_ys(x3, x4, x5), x2, x1) -> cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(x3, x4, x5, bot[7]), x2) zipwith_l#3(x8, x4) -> zipwith_l_f_xs_ys(plus, x8, x4) main(x12) -> cond_take_l_n_xs(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x12) 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: fibs_2#1(zipwith_l, plus, tail_l, x3) -> ConsL(S(0'), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))) cond_take_l_n_xs(ConsL(x16, x18), 0') -> Nil cond_take_l_n_xs(ConsL(x7, fibs_2(x4, x8, x12)), S(x16)) -> Cons(x7, cond_take_l_n_xs(fibs_2#1(x4, x8, x12, bot[0]), x16)) cond_take_l_n_xs(ConsL(x7, zipwith_l_f_xs_ys(x4, x8, x12)), S(x16)) -> Cons(x7, cond_take_l_n_xs(zipwith_l_f_xs_ys#1(x4, x8, x12, bot[0]), x16)) plus#2(0', x12) -> x12 plus#2(S(x4), x2) -> S(plus#2(x4, x2)) cond_zipwith_l_f_xs_ys_1(ConsL(x4, x3), x2, x1) -> ConsL(plus#2(x2, x4), zipwith_l#3(x1, x3)) cond_zipwith_l_f_xs_ys(ConsL(x5, x4), zipwith_l_f_xs_ys(x1, x2, x3)) -> cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(x1, x2, x3, bot[6]), x5, x4) cond_zipwith_l_f_xs_ys(ConsL(x5, x4), fibs_2(x1, x2, x3)) -> cond_zipwith_l_f_xs_ys_1(fibs_2#1(x1, x2, x3, bot[6]), x5, x4) zipwith_l_f_xs_ys#1(plus, fibs, x5, x3) -> cond_zipwith_l_f_xs_ys(ConsL(0', fibs_2(zipwith_l, plus, tail_l)), x5) zipwith_l_f_xs_ys#1(plus, fibs_2(x3, x4, x5), x2, x1) -> cond_zipwith_l_f_xs_ys(fibs_2#1(x3, x4, x5, bot[7]), x2) zipwith_l_f_xs_ys#1(plus, zipwith_l_f_xs_ys(x3, x4, x5), x2, x1) -> cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(x3, x4, x5, bot[7]), x2) zipwith_l#3(x8, x4) -> zipwith_l_f_xs_ys(plus, x8, x4) main(x12) -> cond_take_l_n_xs(ConsL(0', fibs_2(zipwith_l, plus, tail_l)), x12) 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: fibs_2#1(zipwith_l, plus, tail_l, x3) -> ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))) cond_take_l_n_xs(ConsL(x16, x18), 0) -> Nil cond_take_l_n_xs(ConsL(x7, fibs_2(x4, x8, x12)), S(x16)) -> Cons(x7, cond_take_l_n_xs(fibs_2#1(x4, x8, x12, bot[0]), x16)) cond_take_l_n_xs(ConsL(x7, zipwith_l_f_xs_ys(x4, x8, x12)), S(x16)) -> Cons(x7, cond_take_l_n_xs(zipwith_l_f_xs_ys#1(x4, x8, x12, bot[0]), x16)) plus#2(0, x12) -> x12 plus#2(S(x4), x2) -> S(plus#2(x4, x2)) cond_zipwith_l_f_xs_ys_1(ConsL(x4, x3), x2, x1) -> ConsL(plus#2(x2, x4), zipwith_l#3(x1, x3)) cond_zipwith_l_f_xs_ys(ConsL(x5, x4), zipwith_l_f_xs_ys(x1, x2, x3)) -> cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(x1, x2, x3, bot[6]), x5, x4) cond_zipwith_l_f_xs_ys(ConsL(x5, x4), fibs_2(x1, x2, x3)) -> cond_zipwith_l_f_xs_ys_1(fibs_2#1(x1, x2, x3, bot[6]), x5, x4) zipwith_l_f_xs_ys#1(plus, fibs, x5, x3) -> cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x5) zipwith_l_f_xs_ys#1(plus, fibs_2(x3, x4, x5), x2, x1) -> cond_zipwith_l_f_xs_ys(fibs_2#1(x3, x4, x5, bot[7]), x2) zipwith_l_f_xs_ys#1(plus, zipwith_l_f_xs_ys(x3, x4, x5), x2, x1) -> cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(x3, x4, x5, bot[7]), x2) zipwith_l#3(x8, x4) -> zipwith_l_f_xs_ys(plus, x8, x4) main(x12) -> cond_take_l_n_xs(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x12) 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: fibs_2#1(zipwith_l, plus, tail_l, x3) -> ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))) [1] cond_take_l_n_xs(ConsL(x16, x18), 0) -> Nil [1] cond_take_l_n_xs(ConsL(x7, fibs_2(x4, x8, x12)), S(x16)) -> Cons(x7, cond_take_l_n_xs(fibs_2#1(x4, x8, x12, bot[0]), x16)) [1] cond_take_l_n_xs(ConsL(x7, zipwith_l_f_xs_ys(x4, x8, x12)), S(x16)) -> Cons(x7, cond_take_l_n_xs(zipwith_l_f_xs_ys#1(x4, x8, x12, bot[0]), x16)) [1] plus#2(0, x12) -> x12 [1] plus#2(S(x4), x2) -> S(plus#2(x4, x2)) [1] cond_zipwith_l_f_xs_ys_1(ConsL(x4, x3), x2, x1) -> ConsL(plus#2(x2, x4), zipwith_l#3(x1, x3)) [1] cond_zipwith_l_f_xs_ys(ConsL(x5, x4), zipwith_l_f_xs_ys(x1, x2, x3)) -> cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(x1, x2, x3, bot[6]), x5, x4) [1] cond_zipwith_l_f_xs_ys(ConsL(x5, x4), fibs_2(x1, x2, x3)) -> cond_zipwith_l_f_xs_ys_1(fibs_2#1(x1, x2, x3, bot[6]), x5, x4) [1] zipwith_l_f_xs_ys#1(plus, fibs, x5, x3) -> cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x5) [1] zipwith_l_f_xs_ys#1(plus, fibs_2(x3, x4, x5), x2, x1) -> cond_zipwith_l_f_xs_ys(fibs_2#1(x3, x4, x5, bot[7]), x2) [1] zipwith_l_f_xs_ys#1(plus, zipwith_l_f_xs_ys(x3, x4, x5), x2, x1) -> cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(x3, x4, x5, bot[7]), x2) [1] zipwith_l#3(x8, x4) -> zipwith_l_f_xs_ys(plus, x8, x4) [1] main(x12) -> cond_take_l_n_xs(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x12) [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: fibs_2#1(zipwith_l, plus, tail_l, x3) -> ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))) [1] cond_take_l_n_xs(ConsL(x16, x18), 0) -> Nil [1] cond_take_l_n_xs(ConsL(x7, fibs_2(x4, x8, x12)), S(x16)) -> Cons(x7, cond_take_l_n_xs(fibs_2#1(x4, x8, x12, bot[0]), x16)) [1] cond_take_l_n_xs(ConsL(x7, zipwith_l_f_xs_ys(x4, x8, x12)), S(x16)) -> Cons(x7, cond_take_l_n_xs(zipwith_l_f_xs_ys#1(x4, x8, x12, bot[0]), x16)) [1] plus#2(0, x12) -> x12 [1] plus#2(S(x4), x2) -> S(plus#2(x4, x2)) [1] cond_zipwith_l_f_xs_ys_1(ConsL(x4, x3), x2, x1) -> ConsL(plus#2(x2, x4), zipwith_l#3(x1, x3)) [1] cond_zipwith_l_f_xs_ys(ConsL(x5, x4), zipwith_l_f_xs_ys(x1, x2, x3)) -> cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(x1, x2, x3, bot[6]), x5, x4) [1] cond_zipwith_l_f_xs_ys(ConsL(x5, x4), fibs_2(x1, x2, x3)) -> cond_zipwith_l_f_xs_ys_1(fibs_2#1(x1, x2, x3, bot[6]), x5, x4) [1] zipwith_l_f_xs_ys#1(plus, fibs, x5, x3) -> cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x5) [1] zipwith_l_f_xs_ys#1(plus, fibs_2(x3, x4, x5), x2, x1) -> cond_zipwith_l_f_xs_ys(fibs_2#1(x3, x4, x5, bot[7]), x2) [1] zipwith_l_f_xs_ys#1(plus, zipwith_l_f_xs_ys(x3, x4, x5), x2, x1) -> cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(x3, x4, x5, bot[7]), x2) [1] zipwith_l#3(x8, x4) -> zipwith_l_f_xs_ys(plus, x8, x4) [1] main(x12) -> cond_take_l_n_xs(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x12) [1] The TRS has the following type information: fibs_2#1 :: zipwith_l -> plus -> tail_l -> bot[0]:bot[6]:bot[7] -> ConsL zipwith_l :: zipwith_l plus :: plus tail_l :: tail_l ConsL :: 0:S -> fibs:fibs_2:zipwith_l_f_xs_ys -> ConsL S :: 0:S -> 0:S 0 :: 0:S zipwith_l#3 :: fibs:fibs_2:zipwith_l_f_xs_ys -> fibs:fibs_2:zipwith_l_f_xs_ys -> fibs:fibs_2:zipwith_l_f_xs_ys fibs :: fibs:fibs_2:zipwith_l_f_xs_ys fibs_2 :: zipwith_l -> plus -> tail_l -> fibs:fibs_2:zipwith_l_f_xs_ys cond_take_l_n_xs :: ConsL -> 0:S -> Nil:Cons Nil :: Nil:Cons Cons :: 0:S -> Nil:Cons -> Nil:Cons bot[0] :: bot[0]:bot[6]:bot[7] zipwith_l_f_xs_ys :: plus -> fibs:fibs_2:zipwith_l_f_xs_ys -> fibs:fibs_2:zipwith_l_f_xs_ys -> fibs:fibs_2:zipwith_l_f_xs_ys zipwith_l_f_xs_ys#1 :: plus -> fibs:fibs_2:zipwith_l_f_xs_ys -> fibs:fibs_2:zipwith_l_f_xs_ys -> bot[0]:bot[6]:bot[7] -> ConsL plus#2 :: 0:S -> 0:S -> 0:S cond_zipwith_l_f_xs_ys_1 :: ConsL -> 0:S -> fibs:fibs_2:zipwith_l_f_xs_ys -> ConsL cond_zipwith_l_f_xs_ys :: ConsL -> fibs:fibs_2:zipwith_l_f_xs_ys -> ConsL bot[6] :: bot[0]:bot[6]:bot[7] bot[7] :: bot[0]:bot[6]:bot[7] main :: 0:S -> Nil:Cons 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: cond_take_l_n_xs_2 main_1 (c) The following functions are completely defined: zipwith_l_f_xs_ys#1_4 fibs_2#1_4 cond_zipwith_l_f_xs_ys_2 cond_zipwith_l_f_xs_ys_1_3 plus#2_2 zipwith_l#3_2 Due to the following rules being added: cond_zipwith_l_f_xs_ys(v0, v1) -> const [0] cond_zipwith_l_f_xs_ys_1(v0, v1, v2) -> const [0] And the following fresh constants: const ---------------------------------------- (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: fibs_2#1(zipwith_l, plus, tail_l, x3) -> ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))) [1] cond_take_l_n_xs(ConsL(x16, x18), 0) -> Nil [1] cond_take_l_n_xs(ConsL(x7, fibs_2(x4, x8, x12)), S(x16)) -> Cons(x7, cond_take_l_n_xs(fibs_2#1(x4, x8, x12, bot[0]), x16)) [1] cond_take_l_n_xs(ConsL(x7, zipwith_l_f_xs_ys(x4, x8, x12)), S(x16)) -> Cons(x7, cond_take_l_n_xs(zipwith_l_f_xs_ys#1(x4, x8, x12, bot[0]), x16)) [1] plus#2(0, x12) -> x12 [1] plus#2(S(x4), x2) -> S(plus#2(x4, x2)) [1] cond_zipwith_l_f_xs_ys_1(ConsL(x4, x3), x2, x1) -> ConsL(plus#2(x2, x4), zipwith_l#3(x1, x3)) [1] cond_zipwith_l_f_xs_ys(ConsL(x5, x4), zipwith_l_f_xs_ys(x1, x2, x3)) -> cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(x1, x2, x3, bot[6]), x5, x4) [1] cond_zipwith_l_f_xs_ys(ConsL(x5, x4), fibs_2(x1, x2, x3)) -> cond_zipwith_l_f_xs_ys_1(fibs_2#1(x1, x2, x3, bot[6]), x5, x4) [1] zipwith_l_f_xs_ys#1(plus, fibs, x5, x3) -> cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x5) [1] zipwith_l_f_xs_ys#1(plus, fibs_2(x3, x4, x5), x2, x1) -> cond_zipwith_l_f_xs_ys(fibs_2#1(x3, x4, x5, bot[7]), x2) [1] zipwith_l_f_xs_ys#1(plus, zipwith_l_f_xs_ys(x3, x4, x5), x2, x1) -> cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(x3, x4, x5, bot[7]), x2) [1] zipwith_l#3(x8, x4) -> zipwith_l_f_xs_ys(plus, x8, x4) [1] main(x12) -> cond_take_l_n_xs(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x12) [1] cond_zipwith_l_f_xs_ys(v0, v1) -> const [0] cond_zipwith_l_f_xs_ys_1(v0, v1, v2) -> const [0] The TRS has the following type information: fibs_2#1 :: zipwith_l -> plus -> tail_l -> bot[0]:bot[6]:bot[7] -> ConsL:const zipwith_l :: zipwith_l plus :: plus tail_l :: tail_l ConsL :: 0:S -> fibs:fibs_2:zipwith_l_f_xs_ys -> ConsL:const S :: 0:S -> 0:S 0 :: 0:S zipwith_l#3 :: fibs:fibs_2:zipwith_l_f_xs_ys -> fibs:fibs_2:zipwith_l_f_xs_ys -> fibs:fibs_2:zipwith_l_f_xs_ys fibs :: fibs:fibs_2:zipwith_l_f_xs_ys fibs_2 :: zipwith_l -> plus -> tail_l -> fibs:fibs_2:zipwith_l_f_xs_ys cond_take_l_n_xs :: ConsL:const -> 0:S -> Nil:Cons Nil :: Nil:Cons Cons :: 0:S -> Nil:Cons -> Nil:Cons bot[0] :: bot[0]:bot[6]:bot[7] zipwith_l_f_xs_ys :: plus -> fibs:fibs_2:zipwith_l_f_xs_ys -> fibs:fibs_2:zipwith_l_f_xs_ys -> fibs:fibs_2:zipwith_l_f_xs_ys zipwith_l_f_xs_ys#1 :: plus -> fibs:fibs_2:zipwith_l_f_xs_ys -> fibs:fibs_2:zipwith_l_f_xs_ys -> bot[0]:bot[6]:bot[7] -> ConsL:const plus#2 :: 0:S -> 0:S -> 0:S cond_zipwith_l_f_xs_ys_1 :: ConsL:const -> 0:S -> fibs:fibs_2:zipwith_l_f_xs_ys -> ConsL:const cond_zipwith_l_f_xs_ys :: ConsL:const -> fibs:fibs_2:zipwith_l_f_xs_ys -> ConsL:const bot[6] :: bot[0]:bot[6]:bot[7] bot[7] :: bot[0]:bot[6]:bot[7] main :: 0:S -> Nil:Cons const :: ConsL:const 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: fibs_2#1(zipwith_l, plus, tail_l, x3) -> ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))) [1] cond_take_l_n_xs(ConsL(x16, x18), 0) -> Nil [1] cond_take_l_n_xs(ConsL(x7, fibs_2(zipwith_l, plus, tail_l)), S(x16)) -> Cons(x7, cond_take_l_n_xs(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x16)) [2] cond_take_l_n_xs(ConsL(x7, zipwith_l_f_xs_ys(plus, fibs, x12)), S(x16)) -> Cons(x7, cond_take_l_n_xs(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x12), x16)) [2] cond_take_l_n_xs(ConsL(x7, zipwith_l_f_xs_ys(plus, fibs_2(x3', x4', x5'), x12)), S(x16)) -> Cons(x7, cond_take_l_n_xs(cond_zipwith_l_f_xs_ys(fibs_2#1(x3', x4', x5', bot[7]), x12), x16)) [2] cond_take_l_n_xs(ConsL(x7, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x3'', x4'', x5''), x12)), S(x16)) -> Cons(x7, cond_take_l_n_xs(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(x3'', x4'', x5'', bot[7]), x12), x16)) [2] plus#2(0, x12) -> x12 [1] plus#2(S(x4), x2) -> S(plus#2(x4, x2)) [1] cond_zipwith_l_f_xs_ys_1(ConsL(x4, x3), x2, x1) -> ConsL(plus#2(x2, x4), zipwith_l#3(x1, x3)) [1] cond_zipwith_l_f_xs_ys(ConsL(x5, x4), zipwith_l_f_xs_ys(plus, fibs, x3)) -> cond_zipwith_l_f_xs_ys_1(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x3), x5, x4) [2] cond_zipwith_l_f_xs_ys(ConsL(x5, x4), zipwith_l_f_xs_ys(plus, fibs_2(x31, x41, x51), x3)) -> cond_zipwith_l_f_xs_ys_1(cond_zipwith_l_f_xs_ys(fibs_2#1(x31, x41, x51, bot[7]), x3), x5, x4) [2] cond_zipwith_l_f_xs_ys(ConsL(x5, x4), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x32, x42, x52), x3)) -> cond_zipwith_l_f_xs_ys_1(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(x32, x42, x52, bot[7]), x3), x5, x4) [2] cond_zipwith_l_f_xs_ys(ConsL(x5, x4), fibs_2(zipwith_l, plus, tail_l)) -> cond_zipwith_l_f_xs_ys_1(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x5, x4) [2] zipwith_l_f_xs_ys#1(plus, fibs, x5, x3) -> cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x5) [1] zipwith_l_f_xs_ys#1(plus, fibs_2(zipwith_l, plus, tail_l), x2, x1) -> cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x2) [2] zipwith_l_f_xs_ys#1(plus, zipwith_l_f_xs_ys(plus, fibs, x5), x2, x1) -> cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x5), x2) [2] zipwith_l_f_xs_ys#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x33, x43, x53), x5), x2, x1) -> cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(x33, x43, x53, bot[7]), x5), x2) [2] zipwith_l_f_xs_ys#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x34, x44, x54), x5), x2, x1) -> cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(x34, x44, x54, bot[7]), x5), x2) [2] zipwith_l#3(x8, x4) -> zipwith_l_f_xs_ys(plus, x8, x4) [1] main(x12) -> cond_take_l_n_xs(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x12) [1] cond_zipwith_l_f_xs_ys(v0, v1) -> const [0] cond_zipwith_l_f_xs_ys_1(v0, v1, v2) -> const [0] The TRS has the following type information: fibs_2#1 :: zipwith_l -> plus -> tail_l -> bot[0]:bot[6]:bot[7] -> ConsL:const zipwith_l :: zipwith_l plus :: plus tail_l :: tail_l ConsL :: 0:S -> fibs:fibs_2:zipwith_l_f_xs_ys -> ConsL:const S :: 0:S -> 0:S 0 :: 0:S zipwith_l#3 :: fibs:fibs_2:zipwith_l_f_xs_ys -> fibs:fibs_2:zipwith_l_f_xs_ys -> fibs:fibs_2:zipwith_l_f_xs_ys fibs :: fibs:fibs_2:zipwith_l_f_xs_ys fibs_2 :: zipwith_l -> plus -> tail_l -> fibs:fibs_2:zipwith_l_f_xs_ys cond_take_l_n_xs :: ConsL:const -> 0:S -> Nil:Cons Nil :: Nil:Cons Cons :: 0:S -> Nil:Cons -> Nil:Cons bot[0] :: bot[0]:bot[6]:bot[7] zipwith_l_f_xs_ys :: plus -> fibs:fibs_2:zipwith_l_f_xs_ys -> fibs:fibs_2:zipwith_l_f_xs_ys -> fibs:fibs_2:zipwith_l_f_xs_ys zipwith_l_f_xs_ys#1 :: plus -> fibs:fibs_2:zipwith_l_f_xs_ys -> fibs:fibs_2:zipwith_l_f_xs_ys -> bot[0]:bot[6]:bot[7] -> ConsL:const plus#2 :: 0:S -> 0:S -> 0:S cond_zipwith_l_f_xs_ys_1 :: ConsL:const -> 0:S -> fibs:fibs_2:zipwith_l_f_xs_ys -> ConsL:const cond_zipwith_l_f_xs_ys :: ConsL:const -> fibs:fibs_2:zipwith_l_f_xs_ys -> ConsL:const bot[6] :: bot[0]:bot[6]:bot[7] bot[7] :: bot[0]:bot[6]:bot[7] main :: 0:S -> Nil:Cons const :: ConsL:const 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: zipwith_l => 0 plus => 0 tail_l => 0 0 => 0 fibs => 0 Nil => 0 bot[0] => 0 bot[6] => 1 bot[7] => 2 const => 0 ---------------------------------------- (14) Obligation: Complexity RNTS consisting of the following rules: cond_take_l_n_xs(z, z') -{ 1 }-> 0 :|: z = 1 + x16 + x18, x18 >= 0, x16 >= 0, z' = 0 cond_take_l_n_xs(z, z') -{ 2 }-> 1 + x7 + cond_take_l_n_xs(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(x3'', x4'', x5'', 2), x12), x16) :|: x4'' >= 0, x5'' >= 0, x7 >= 0, x12 >= 0, z = 1 + x7 + (1 + 0 + (1 + x3'' + x4'' + x5'') + x12), x3'' >= 0, x16 >= 0, z' = 1 + x16 cond_take_l_n_xs(z, z') -{ 2 }-> 1 + x7 + cond_take_l_n_xs(cond_zipwith_l_f_xs_ys(fibs_2#1(x3', x4', x5', 2), x12), x16) :|: x7 >= 0, z = 1 + x7 + (1 + 0 + (1 + x3' + x4' + x5') + x12), x12 >= 0, x5' >= 0, x3' >= 0, x4' >= 0, x16 >= 0, z' = 1 + x16 cond_take_l_n_xs(z, z') -{ 2 }-> 1 + x7 + cond_take_l_n_xs(cond_zipwith_l_f_xs_ys(1 + 0 + (1 + 0 + 0 + 0), x12), x16) :|: x7 >= 0, z = 1 + x7 + (1 + 0 + 0 + x12), x12 >= 0, x16 >= 0, z' = 1 + x16 cond_take_l_n_xs(z, z') -{ 2 }-> 1 + x7 + cond_take_l_n_xs(1 + (1 + 0) + zipwith_l#3(0, 1 + 0 + 0 + 0), x16) :|: x7 >= 0, z = 1 + x7 + (1 + 0 + 0 + 0), x16 >= 0, z' = 1 + x16 cond_zipwith_l_f_xs_ys(z, z') -{ 2 }-> cond_zipwith_l_f_xs_ys_1(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(x32, x42, x52, 2), x3), x5, x4) :|: x5 >= 0, x4 >= 0, x32 >= 0, x52 >= 0, z' = 1 + 0 + (1 + x32 + x42 + x52) + x3, x42 >= 0, z = 1 + x5 + x4, x3 >= 0 cond_zipwith_l_f_xs_ys(z, z') -{ 2 }-> cond_zipwith_l_f_xs_ys_1(cond_zipwith_l_f_xs_ys(fibs_2#1(x31, x41, x51, 2), x3), x5, x4) :|: x5 >= 0, x4 >= 0, x41 >= 0, x31 >= 0, x51 >= 0, z = 1 + x5 + x4, z' = 1 + 0 + (1 + x31 + x41 + x51) + x3, x3 >= 0 cond_zipwith_l_f_xs_ys(z, z') -{ 2 }-> cond_zipwith_l_f_xs_ys_1(cond_zipwith_l_f_xs_ys(1 + 0 + (1 + 0 + 0 + 0), x3), x5, x4) :|: x5 >= 0, x4 >= 0, z = 1 + x5 + x4, z' = 1 + 0 + 0 + x3, x3 >= 0 cond_zipwith_l_f_xs_ys(z, z') -{ 2 }-> cond_zipwith_l_f_xs_ys_1(1 + (1 + 0) + zipwith_l#3(0, 1 + 0 + 0 + 0), x5, x4) :|: x5 >= 0, x4 >= 0, z' = 1 + 0 + 0 + 0, z = 1 + x5 + x4 cond_zipwith_l_f_xs_ys(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 cond_zipwith_l_f_xs_ys_1(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 cond_zipwith_l_f_xs_ys_1(z, z', z'') -{ 1 }-> 1 + plus#2(x2, x4) + zipwith_l#3(x1, x3) :|: z'' = x1, z' = x2, x4 >= 0, x1 >= 0, z = 1 + x4 + x3, x3 >= 0, x2 >= 0 fibs_2#1(z, z', z'', z1) -{ 1 }-> 1 + (1 + 0) + zipwith_l#3(0, 1 + 0 + 0 + 0) :|: z'' = 0, z1 = x3, z = 0, x3 >= 0, z' = 0 main(z) -{ 1 }-> cond_take_l_n_xs(1 + 0 + (1 + 0 + 0 + 0), x12) :|: x12 >= 0, z = x12 plus#2(z, z') -{ 1 }-> x12 :|: x12 >= 0, z = 0, z' = x12 plus#2(z, z') -{ 1 }-> 1 + plus#2(x4, x2) :|: z' = x2, x4 >= 0, z = 1 + x4, x2 >= 0 zipwith_l#3(z, z') -{ 1 }-> 1 + 0 + x8 + x4 :|: z = x8, x4 >= 0, x8 >= 0, z' = x4 zipwith_l_f_xs_ys#1(z, z', z'', z1) -{ 2 }-> cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(x34, x44, x54, 2), x5), x2) :|: x44 >= 0, z' = 1 + 0 + (1 + x34 + x44 + x54) + x5, x34 >= 0, x54 >= 0, x5 >= 0, x1 >= 0, z1 = x1, z = 0, z'' = x2, x2 >= 0 zipwith_l_f_xs_ys#1(z, z', z'', z1) -{ 2 }-> cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(x33, x43, x53, 2), x5), x2) :|: x33 >= 0, x5 >= 0, x1 >= 0, z' = 1 + 0 + (1 + x33 + x43 + x53) + x5, x43 >= 0, z1 = x1, x53 >= 0, z = 0, z'' = x2, x2 >= 0 zipwith_l_f_xs_ys#1(z, z', z'', z1) -{ 2 }-> cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(1 + 0 + (1 + 0 + 0 + 0), x5), x2) :|: x5 >= 0, x1 >= 0, z' = 1 + 0 + 0 + x5, z1 = x1, z = 0, z'' = x2, x2 >= 0 zipwith_l_f_xs_ys#1(z, z', z'', z1) -{ 1 }-> cond_zipwith_l_f_xs_ys(1 + 0 + (1 + 0 + 0 + 0), x5) :|: x5 >= 0, z'' = x5, z1 = x3, z = 0, x3 >= 0, z' = 0 zipwith_l_f_xs_ys#1(z, z', z'', z1) -{ 2 }-> cond_zipwith_l_f_xs_ys(1 + (1 + 0) + zipwith_l#3(0, 1 + 0 + 0 + 0), x2) :|: x1 >= 0, z' = 1 + 0 + 0 + 0, z1 = x1, z = 0, z'' = x2, x2 >= 0 ---------------------------------------- (15) InliningProof (UPPER BOUND(ID)) Inlined the following terminating rules on right-hand sides where appropriate: zipwith_l#3(z, z') -{ 1 }-> 1 + 0 + x8 + x4 :|: z = x8, x4 >= 0, x8 >= 0, z' = x4 fibs_2#1(z, z', z'', z1) -{ 1 }-> 1 + (1 + 0) + zipwith_l#3(0, 1 + 0 + 0 + 0) :|: z'' = 0, z1 = x3, z = 0, x3 >= 0, z' = 0 ---------------------------------------- (16) Obligation: Complexity RNTS consisting of the following rules: cond_take_l_n_xs(z, z') -{ 1 }-> 0 :|: z = 1 + x16 + x18, x18 >= 0, x16 >= 0, z' = 0 cond_take_l_n_xs(z, z') -{ 2 }-> 1 + x7 + cond_take_l_n_xs(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(x3'', x4'', x5'', 2), x12), x16) :|: x4'' >= 0, x5'' >= 0, x7 >= 0, x12 >= 0, z = 1 + x7 + (1 + 0 + (1 + x3'' + x4'' + x5'') + x12), x3'' >= 0, x16 >= 0, z' = 1 + x16 cond_take_l_n_xs(z, z') -{ 2 }-> 1 + x7 + cond_take_l_n_xs(cond_zipwith_l_f_xs_ys(1 + 0 + (1 + 0 + 0 + 0), x12), x16) :|: x7 >= 0, z = 1 + x7 + (1 + 0 + 0 + x12), x12 >= 0, x16 >= 0, z' = 1 + x16 cond_take_l_n_xs(z, z') -{ 3 }-> 1 + x7 + cond_take_l_n_xs(cond_zipwith_l_f_xs_ys(1 + (1 + 0) + zipwith_l#3(0, 1 + 0 + 0 + 0), x12), x16) :|: x7 >= 0, z = 1 + x7 + (1 + 0 + (1 + x3' + x4' + x5') + x12), x12 >= 0, x5' >= 0, x3' >= 0, x4' >= 0, x16 >= 0, z' = 1 + x16, x5' = 0, 2 = x3, x3' = 0, x3 >= 0, x4' = 0 cond_take_l_n_xs(z, z') -{ 3 }-> 1 + x7 + cond_take_l_n_xs(1 + (1 + 0) + (1 + 0 + x8 + x4), x16) :|: x7 >= 0, z = 1 + x7 + (1 + 0 + 0 + 0), x16 >= 0, z' = 1 + x16, 0 = x8, x4 >= 0, x8 >= 0, 1 + 0 + 0 + 0 = x4 cond_zipwith_l_f_xs_ys(z, z') -{ 2 }-> cond_zipwith_l_f_xs_ys_1(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(x32, x42, x52, 2), x3), x5, x4) :|: x5 >= 0, x4 >= 0, x32 >= 0, x52 >= 0, z' = 1 + 0 + (1 + x32 + x42 + x52) + x3, x42 >= 0, z = 1 + x5 + x4, x3 >= 0 cond_zipwith_l_f_xs_ys(z, z') -{ 2 }-> cond_zipwith_l_f_xs_ys_1(cond_zipwith_l_f_xs_ys(1 + 0 + (1 + 0 + 0 + 0), x3), x5, x4) :|: x5 >= 0, x4 >= 0, z = 1 + x5 + x4, z' = 1 + 0 + 0 + x3, x3 >= 0 cond_zipwith_l_f_xs_ys(z, z') -{ 3 }-> cond_zipwith_l_f_xs_ys_1(cond_zipwith_l_f_xs_ys(1 + (1 + 0) + zipwith_l#3(0, 1 + 0 + 0 + 0), x3), x5, x4) :|: x5 >= 0, x4 >= 0, x41 >= 0, x31 >= 0, x51 >= 0, z = 1 + x5 + x4, z' = 1 + 0 + (1 + x31 + x41 + x51) + x3, x3 >= 0, x51 = 0, 2 = x3', x31 = 0, x3' >= 0, x41 = 0 cond_zipwith_l_f_xs_ys(z, z') -{ 3 }-> cond_zipwith_l_f_xs_ys_1(1 + (1 + 0) + (1 + 0 + x8 + x4'), x5, x4) :|: x5 >= 0, x4 >= 0, z' = 1 + 0 + 0 + 0, z = 1 + x5 + x4, 0 = x8, x4' >= 0, x8 >= 0, 1 + 0 + 0 + 0 = x4' cond_zipwith_l_f_xs_ys(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 cond_zipwith_l_f_xs_ys_1(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 cond_zipwith_l_f_xs_ys_1(z, z', z'') -{ 2 }-> 1 + plus#2(x2, x4) + (1 + 0 + x8 + x4') :|: z'' = x1, z' = x2, x4 >= 0, x1 >= 0, z = 1 + x4 + x3, x3 >= 0, x2 >= 0, x1 = x8, x4' >= 0, x8 >= 0, x3 = x4' fibs_2#1(z, z', z'', z1) -{ 2 }-> 1 + (1 + 0) + (1 + 0 + x8 + x4) :|: z'' = 0, z1 = x3, z = 0, x3 >= 0, z' = 0, 0 = x8, x4 >= 0, x8 >= 0, 1 + 0 + 0 + 0 = x4 main(z) -{ 1 }-> cond_take_l_n_xs(1 + 0 + (1 + 0 + 0 + 0), x12) :|: x12 >= 0, z = x12 plus#2(z, z') -{ 1 }-> x12 :|: x12 >= 0, z = 0, z' = x12 plus#2(z, z') -{ 1 }-> 1 + plus#2(x4, x2) :|: z' = x2, x4 >= 0, z = 1 + x4, x2 >= 0 zipwith_l#3(z, z') -{ 1 }-> 1 + 0 + x8 + x4 :|: z = x8, x4 >= 0, x8 >= 0, z' = x4 zipwith_l_f_xs_ys#1(z, z', z'', z1) -{ 2 }-> cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(x34, x44, x54, 2), x5), x2) :|: x44 >= 0, z' = 1 + 0 + (1 + x34 + x44 + x54) + x5, x34 >= 0, x54 >= 0, x5 >= 0, x1 >= 0, z1 = x1, z = 0, z'' = x2, x2 >= 0 zipwith_l_f_xs_ys#1(z, z', z'', z1) -{ 2 }-> cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(1 + 0 + (1 + 0 + 0 + 0), x5), x2) :|: x5 >= 0, x1 >= 0, z' = 1 + 0 + 0 + x5, z1 = x1, z = 0, z'' = x2, x2 >= 0 zipwith_l_f_xs_ys#1(z, z', z'', z1) -{ 3 }-> cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(1 + (1 + 0) + zipwith_l#3(0, 1 + 0 + 0 + 0), x5), x2) :|: x33 >= 0, x5 >= 0, x1 >= 0, z' = 1 + 0 + (1 + x33 + x43 + x53) + x5, x43 >= 0, z1 = x1, x53 >= 0, z = 0, z'' = x2, x2 >= 0, x53 = 0, 2 = x3, x33 = 0, x3 >= 0, x43 = 0 zipwith_l_f_xs_ys#1(z, z', z'', z1) -{ 1 }-> cond_zipwith_l_f_xs_ys(1 + 0 + (1 + 0 + 0 + 0), x5) :|: x5 >= 0, z'' = x5, z1 = x3, z = 0, x3 >= 0, z' = 0 zipwith_l_f_xs_ys#1(z, z', z'', z1) -{ 3 }-> cond_zipwith_l_f_xs_ys(1 + (1 + 0) + (1 + 0 + x8 + x4), x2) :|: x1 >= 0, z' = 1 + 0 + 0 + 0, z1 = x1, z = 0, z'' = x2, x2 >= 0, 0 = x8, x4 >= 0, x8 >= 0, 1 + 0 + 0 + 0 = x4 ---------------------------------------- (17) SimplificationProof (BOTH BOUNDS(ID, ID)) Simplified the RNTS by moving equalities from the constraints into the right-hand sides. ---------------------------------------- (18) Obligation: Complexity RNTS consisting of the following rules: cond_take_l_n_xs(z, z') -{ 1 }-> 0 :|: z = 1 + x16 + x18, x18 >= 0, x16 >= 0, z' = 0 cond_take_l_n_xs(z, z') -{ 2 }-> 1 + x7 + cond_take_l_n_xs(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(x3'', x4'', x5'', 2), x12), z' - 1) :|: x4'' >= 0, x5'' >= 0, x7 >= 0, x12 >= 0, z = 1 + x7 + (1 + 0 + (1 + x3'' + x4'' + x5'') + x12), x3'' >= 0, z' - 1 >= 0 cond_take_l_n_xs(z, z') -{ 2 }-> 1 + x7 + cond_take_l_n_xs(cond_zipwith_l_f_xs_ys(1 + 0 + (1 + 0 + 0 + 0), x12), z' - 1) :|: x7 >= 0, z = 1 + x7 + (1 + 0 + 0 + x12), x12 >= 0, z' - 1 >= 0 cond_take_l_n_xs(z, z') -{ 3 }-> 1 + x7 + cond_take_l_n_xs(cond_zipwith_l_f_xs_ys(1 + (1 + 0) + zipwith_l#3(0, 1 + 0 + 0 + 0), x12), z' - 1) :|: x7 >= 0, z = 1 + x7 + (1 + 0 + (1 + x3' + x4' + x5') + x12), x12 >= 0, x5' >= 0, x3' >= 0, x4' >= 0, z' - 1 >= 0, x5' = 0, 2 = x3, x3' = 0, x3 >= 0, x4' = 0 cond_take_l_n_xs(z, z') -{ 3 }-> 1 + (z - 2) + cond_take_l_n_xs(1 + (1 + 0) + (1 + 0 + x8 + x4), z' - 1) :|: z - 2 >= 0, z' - 1 >= 0, 0 = x8, x4 >= 0, x8 >= 0, 1 + 0 + 0 + 0 = x4 cond_zipwith_l_f_xs_ys(z, z') -{ 2 }-> cond_zipwith_l_f_xs_ys_1(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(x32, x42, x52, 2), x3), x5, x4) :|: x5 >= 0, x4 >= 0, x32 >= 0, x52 >= 0, z' = 1 + 0 + (1 + x32 + x42 + x52) + x3, x42 >= 0, z = 1 + x5 + x4, x3 >= 0 cond_zipwith_l_f_xs_ys(z, z') -{ 2 }-> cond_zipwith_l_f_xs_ys_1(cond_zipwith_l_f_xs_ys(1 + 0 + (1 + 0 + 0 + 0), z' - 1), x5, x4) :|: x5 >= 0, x4 >= 0, z = 1 + x5 + x4, z' - 1 >= 0 cond_zipwith_l_f_xs_ys(z, z') -{ 3 }-> cond_zipwith_l_f_xs_ys_1(cond_zipwith_l_f_xs_ys(1 + (1 + 0) + zipwith_l#3(0, 1 + 0 + 0 + 0), x3), x5, x4) :|: x5 >= 0, x4 >= 0, x41 >= 0, x31 >= 0, x51 >= 0, z = 1 + x5 + x4, z' = 1 + 0 + (1 + x31 + x41 + x51) + x3, x3 >= 0, x51 = 0, 2 = x3', x31 = 0, x3' >= 0, x41 = 0 cond_zipwith_l_f_xs_ys(z, z') -{ 3 }-> cond_zipwith_l_f_xs_ys_1(1 + (1 + 0) + (1 + 0 + x8 + x4'), x5, x4) :|: x5 >= 0, x4 >= 0, z' = 1 + 0 + 0 + 0, z = 1 + x5 + x4, 0 = x8, x4' >= 0, x8 >= 0, 1 + 0 + 0 + 0 = x4' cond_zipwith_l_f_xs_ys(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 cond_zipwith_l_f_xs_ys_1(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 cond_zipwith_l_f_xs_ys_1(z, z', z'') -{ 2 }-> 1 + plus#2(z', x4) + (1 + 0 + z'' + x4') :|: x4 >= 0, z'' >= 0, z = 1 + x4 + x3, x3 >= 0, z' >= 0, x4' >= 0, x3 = x4' fibs_2#1(z, z', z'', z1) -{ 2 }-> 1 + (1 + 0) + (1 + 0 + x8 + x4) :|: z'' = 0, z = 0, z1 >= 0, z' = 0, 0 = x8, x4 >= 0, x8 >= 0, 1 + 0 + 0 + 0 = x4 main(z) -{ 1 }-> cond_take_l_n_xs(1 + 0 + (1 + 0 + 0 + 0), z) :|: z >= 0 plus#2(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0 plus#2(z, z') -{ 1 }-> 1 + plus#2(z - 1, z') :|: z - 1 >= 0, z' >= 0 zipwith_l#3(z, z') -{ 1 }-> 1 + 0 + z + z' :|: z' >= 0, z >= 0 zipwith_l_f_xs_ys#1(z, z', z'', z1) -{ 2 }-> cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(x34, x44, x54, 2), x5), z'') :|: x44 >= 0, z' = 1 + 0 + (1 + x34 + x44 + x54) + x5, x34 >= 0, x54 >= 0, x5 >= 0, z1 >= 0, z = 0, z'' >= 0 zipwith_l_f_xs_ys#1(z, z', z'', z1) -{ 2 }-> cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(1 + 0 + (1 + 0 + 0 + 0), z' - 1), z'') :|: z' - 1 >= 0, z1 >= 0, z = 0, z'' >= 0 zipwith_l_f_xs_ys#1(z, z', z'', z1) -{ 3 }-> cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(1 + (1 + 0) + zipwith_l#3(0, 1 + 0 + 0 + 0), x5), z'') :|: x33 >= 0, x5 >= 0, z1 >= 0, z' = 1 + 0 + (1 + x33 + x43 + x53) + x5, x43 >= 0, x53 >= 0, z = 0, z'' >= 0, x53 = 0, 2 = x3, x33 = 0, x3 >= 0, x43 = 0 zipwith_l_f_xs_ys#1(z, z', z'', z1) -{ 1 }-> cond_zipwith_l_f_xs_ys(1 + 0 + (1 + 0 + 0 + 0), z'') :|: z'' >= 0, z = 0, z1 >= 0, z' = 0 zipwith_l_f_xs_ys#1(z, z', z'', z1) -{ 3 }-> cond_zipwith_l_f_xs_ys(1 + (1 + 0) + (1 + 0 + x8 + x4), z'') :|: z1 >= 0, z' = 1 + 0 + 0 + 0, z = 0, z'' >= 0, 0 = x8, x4 >= 0, x8 >= 0, 1 + 0 + 0 + 0 = x4 ---------------------------------------- (19) CompletionProof (UPPER BOUND(ID)) The TRS is a completely defined constructor system, as every type has a constant constructor and the following rules were added: cond_take_l_n_xs(v0, v1) -> null_cond_take_l_n_xs [0] cond_zipwith_l_f_xs_ys_1(v0, v1, v2) -> null_cond_zipwith_l_f_xs_ys_1 [0] cond_zipwith_l_f_xs_ys(v0, v1) -> null_cond_zipwith_l_f_xs_ys [0] And the following fresh constants: null_cond_take_l_n_xs, null_cond_zipwith_l_f_xs_ys_1, null_cond_zipwith_l_f_xs_ys ---------------------------------------- (20) Obligation: Runtime Complexity Weighted TRS where all functions are completely defined. The underlying TRS is: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: fibs_2#1(zipwith_l, plus, tail_l, x3) -> ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))) [1] cond_take_l_n_xs(ConsL(x16, x18), 0) -> Nil [1] cond_take_l_n_xs(ConsL(x7, fibs_2(x4, x8, x12)), S(x16)) -> Cons(x7, cond_take_l_n_xs(fibs_2#1(x4, x8, x12, bot[0]), x16)) [1] cond_take_l_n_xs(ConsL(x7, zipwith_l_f_xs_ys(x4, x8, x12)), S(x16)) -> Cons(x7, cond_take_l_n_xs(zipwith_l_f_xs_ys#1(x4, x8, x12, bot[0]), x16)) [1] plus#2(0, x12) -> x12 [1] plus#2(S(x4), x2) -> S(plus#2(x4, x2)) [1] cond_zipwith_l_f_xs_ys_1(ConsL(x4, x3), x2, x1) -> ConsL(plus#2(x2, x4), zipwith_l#3(x1, x3)) [1] cond_zipwith_l_f_xs_ys(ConsL(x5, x4), zipwith_l_f_xs_ys(x1, x2, x3)) -> cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(x1, x2, x3, bot[6]), x5, x4) [1] cond_zipwith_l_f_xs_ys(ConsL(x5, x4), fibs_2(x1, x2, x3)) -> cond_zipwith_l_f_xs_ys_1(fibs_2#1(x1, x2, x3, bot[6]), x5, x4) [1] zipwith_l_f_xs_ys#1(plus, fibs, x5, x3) -> cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x5) [1] zipwith_l_f_xs_ys#1(plus, fibs_2(x3, x4, x5), x2, x1) -> cond_zipwith_l_f_xs_ys(fibs_2#1(x3, x4, x5, bot[7]), x2) [1] zipwith_l_f_xs_ys#1(plus, zipwith_l_f_xs_ys(x3, x4, x5), x2, x1) -> cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(x3, x4, x5, bot[7]), x2) [1] zipwith_l#3(x8, x4) -> zipwith_l_f_xs_ys(plus, x8, x4) [1] main(x12) -> cond_take_l_n_xs(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x12) [1] cond_take_l_n_xs(v0, v1) -> null_cond_take_l_n_xs [0] cond_zipwith_l_f_xs_ys_1(v0, v1, v2) -> null_cond_zipwith_l_f_xs_ys_1 [0] cond_zipwith_l_f_xs_ys(v0, v1) -> null_cond_zipwith_l_f_xs_ys [0] The TRS has the following type information: fibs_2#1 :: zipwith_l -> plus -> tail_l -> bot[0]:bot[6]:bot[7] -> ConsL:null_cond_zipwith_l_f_xs_ys_1:null_cond_zipwith_l_f_xs_ys zipwith_l :: zipwith_l plus :: plus tail_l :: tail_l ConsL :: 0:S -> fibs:fibs_2:zipwith_l_f_xs_ys -> ConsL:null_cond_zipwith_l_f_xs_ys_1:null_cond_zipwith_l_f_xs_ys S :: 0:S -> 0:S 0 :: 0:S zipwith_l#3 :: fibs:fibs_2:zipwith_l_f_xs_ys -> fibs:fibs_2:zipwith_l_f_xs_ys -> fibs:fibs_2:zipwith_l_f_xs_ys fibs :: fibs:fibs_2:zipwith_l_f_xs_ys fibs_2 :: zipwith_l -> plus -> tail_l -> fibs:fibs_2:zipwith_l_f_xs_ys cond_take_l_n_xs :: ConsL:null_cond_zipwith_l_f_xs_ys_1:null_cond_zipwith_l_f_xs_ys -> 0:S -> Nil:Cons:null_cond_take_l_n_xs Nil :: Nil:Cons:null_cond_take_l_n_xs Cons :: 0:S -> Nil:Cons:null_cond_take_l_n_xs -> Nil:Cons:null_cond_take_l_n_xs bot[0] :: bot[0]:bot[6]:bot[7] zipwith_l_f_xs_ys :: plus -> fibs:fibs_2:zipwith_l_f_xs_ys -> fibs:fibs_2:zipwith_l_f_xs_ys -> fibs:fibs_2:zipwith_l_f_xs_ys zipwith_l_f_xs_ys#1 :: plus -> fibs:fibs_2:zipwith_l_f_xs_ys -> fibs:fibs_2:zipwith_l_f_xs_ys -> bot[0]:bot[6]:bot[7] -> ConsL:null_cond_zipwith_l_f_xs_ys_1:null_cond_zipwith_l_f_xs_ys plus#2 :: 0:S -> 0:S -> 0:S cond_zipwith_l_f_xs_ys_1 :: ConsL:null_cond_zipwith_l_f_xs_ys_1:null_cond_zipwith_l_f_xs_ys -> 0:S -> fibs:fibs_2:zipwith_l_f_xs_ys -> ConsL:null_cond_zipwith_l_f_xs_ys_1:null_cond_zipwith_l_f_xs_ys cond_zipwith_l_f_xs_ys :: ConsL:null_cond_zipwith_l_f_xs_ys_1:null_cond_zipwith_l_f_xs_ys -> fibs:fibs_2:zipwith_l_f_xs_ys -> ConsL:null_cond_zipwith_l_f_xs_ys_1:null_cond_zipwith_l_f_xs_ys bot[6] :: bot[0]:bot[6]:bot[7] bot[7] :: bot[0]:bot[6]:bot[7] main :: 0:S -> Nil:Cons:null_cond_take_l_n_xs null_cond_take_l_n_xs :: Nil:Cons:null_cond_take_l_n_xs null_cond_zipwith_l_f_xs_ys_1 :: ConsL:null_cond_zipwith_l_f_xs_ys_1:null_cond_zipwith_l_f_xs_ys null_cond_zipwith_l_f_xs_ys :: ConsL:null_cond_zipwith_l_f_xs_ys_1:null_cond_zipwith_l_f_xs_ys Rewrite Strategy: INNERMOST ---------------------------------------- (21) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID)) Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction. The constant constructors are abstracted as follows: zipwith_l => 0 plus => 0 tail_l => 0 0 => 0 fibs => 0 Nil => 0 bot[0] => 0 bot[6] => 1 bot[7] => 2 null_cond_take_l_n_xs => 0 null_cond_zipwith_l_f_xs_ys_1 => 0 null_cond_zipwith_l_f_xs_ys => 0 ---------------------------------------- (22) Obligation: Complexity RNTS consisting of the following rules: cond_take_l_n_xs(z, z') -{ 1 }-> 0 :|: z = 1 + x16 + x18, x18 >= 0, x16 >= 0, z' = 0 cond_take_l_n_xs(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 cond_take_l_n_xs(z, z') -{ 1 }-> 1 + x7 + cond_take_l_n_xs(zipwith_l_f_xs_ys#1(x4, x8, x12, 0), x16) :|: x4 >= 0, x8 >= 0, x7 >= 0, x12 >= 0, z = 1 + x7 + (1 + x4 + x8 + x12), x16 >= 0, z' = 1 + x16 cond_take_l_n_xs(z, z') -{ 1 }-> 1 + x7 + cond_take_l_n_xs(fibs_2#1(x4, x8, x12, 0), x16) :|: x4 >= 0, x8 >= 0, x7 >= 0, x12 >= 0, z = 1 + x7 + (1 + x4 + x8 + x12), x16 >= 0, z' = 1 + x16 cond_zipwith_l_f_xs_ys(z, z') -{ 1 }-> cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(x1, x2, x3, 1), x5, x4) :|: x5 >= 0, x4 >= 0, x1 >= 0, z' = 1 + x1 + x2 + x3, z = 1 + x5 + x4, x2 >= 0, x3 >= 0 cond_zipwith_l_f_xs_ys(z, z') -{ 1 }-> cond_zipwith_l_f_xs_ys_1(fibs_2#1(x1, x2, x3, 1), x5, x4) :|: x5 >= 0, x4 >= 0, x1 >= 0, z' = 1 + x1 + x2 + x3, z = 1 + x5 + x4, x2 >= 0, x3 >= 0 cond_zipwith_l_f_xs_ys(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 cond_zipwith_l_f_xs_ys_1(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 cond_zipwith_l_f_xs_ys_1(z, z', z'') -{ 1 }-> 1 + plus#2(x2, x4) + zipwith_l#3(x1, x3) :|: z'' = x1, z' = x2, x4 >= 0, x1 >= 0, z = 1 + x4 + x3, x3 >= 0, x2 >= 0 fibs_2#1(z, z', z'', z1) -{ 1 }-> 1 + (1 + 0) + zipwith_l#3(0, 1 + 0 + 0 + 0) :|: z'' = 0, z1 = x3, z = 0, x3 >= 0, z' = 0 main(z) -{ 1 }-> cond_take_l_n_xs(1 + 0 + (1 + 0 + 0 + 0), x12) :|: x12 >= 0, z = x12 plus#2(z, z') -{ 1 }-> x12 :|: x12 >= 0, z = 0, z' = x12 plus#2(z, z') -{ 1 }-> 1 + plus#2(x4, x2) :|: z' = x2, x4 >= 0, z = 1 + x4, x2 >= 0 zipwith_l#3(z, z') -{ 1 }-> 1 + 0 + x8 + x4 :|: z = x8, x4 >= 0, x8 >= 0, z' = x4 zipwith_l_f_xs_ys#1(z, z', z'', z1) -{ 1 }-> cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(x3, x4, x5, 2), x2) :|: x4 >= 0, x5 >= 0, x1 >= 0, z' = 1 + x3 + x4 + x5, z1 = x1, z = 0, z'' = x2, x3 >= 0, x2 >= 0 zipwith_l_f_xs_ys#1(z, z', z'', z1) -{ 1 }-> cond_zipwith_l_f_xs_ys(fibs_2#1(x3, x4, x5, 2), x2) :|: x4 >= 0, x5 >= 0, x1 >= 0, z' = 1 + x3 + x4 + x5, z1 = x1, z = 0, z'' = x2, x3 >= 0, x2 >= 0 zipwith_l_f_xs_ys#1(z, z', z'', z1) -{ 1 }-> cond_zipwith_l_f_xs_ys(1 + 0 + (1 + 0 + 0 + 0), x5) :|: x5 >= 0, z'' = x5, z1 = x3, z = 0, x3 >= 0, z' = 0 Only complete derivations are relevant for the runtime complexity. ---------------------------------------- (23) CpxTrsToCdtProof (UPPER BOUND(ID)) Converted Cpx (relative) TRS with rewrite strategy PARALLEL_INNERMOST to CDT ---------------------------------------- (24) Obligation: Complexity Dependency Tuples Problem Rules: fibs_2#1(zipwith_l, plus, tail_l, z0) -> ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))) cond_take_l_n_xs(ConsL(z0, z1), 0) -> Nil cond_take_l_n_xs(ConsL(z0, fibs_2(z1, z2, z3)), S(z4)) -> Cons(z0, cond_take_l_n_xs(fibs_2#1(z1, z2, z3, bot[0]), z4)) cond_take_l_n_xs(ConsL(z0, zipwith_l_f_xs_ys(z1, z2, z3)), S(z4)) -> Cons(z0, cond_take_l_n_xs(zipwith_l_f_xs_ys#1(z1, z2, z3, bot[0]), z4)) plus#2(0, z0) -> z0 plus#2(S(z0), z1) -> S(plus#2(z0, z1)) cond_zipwith_l_f_xs_ys_1(ConsL(z0, z1), z2, z3) -> ConsL(plus#2(z2, z0), zipwith_l#3(z3, z1)) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), zipwith_l_f_xs_ys(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), fibs_2(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), z0, z1) zipwith_l_f_xs_ys#1(plus, fibs, z0, z1) -> cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0) zipwith_l_f_xs_ys#1(plus, fibs_2(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3) zipwith_l_f_xs_ys#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3) zipwith_l#3(z0, z1) -> zipwith_l_f_xs_ys(plus, z0, z1) main(z0) -> cond_take_l_n_xs(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0) Tuples: FIBS_2#1(zipwith_l, plus, tail_l, z0) -> c(ZIPWITH_L#3(fibs, fibs_2(zipwith_l, plus, tail_l))) COND_TAKE_L_N_XS(ConsL(z0, z1), 0) -> c1 COND_TAKE_L_N_XS(ConsL(z0, fibs_2(z1, z2, z3)), S(z4)) -> c2(COND_TAKE_L_N_XS(fibs_2#1(z1, z2, z3, bot[0]), z4), FIBS_2#1(z1, z2, z3, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(z1, z2, z3)), S(z4)) -> c3(COND_TAKE_L_N_XS(zipwith_l_f_xs_ys#1(z1, z2, z3, bot[0]), z4), ZIPWITH_L_F_XS_YS#1(z1, z2, z3, bot[0])) PLUS#2(0, z0) -> c4 PLUS#2(S(z0), z1) -> c5(PLUS#2(z0, z1)) COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c7(ZIPWITH_L#3(z3, z1)) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(z2, z3, z4)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), z0, z1), ZIPWITH_L_F_XS_YS#1(z2, z3, z4, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), fibs_2(z2, z3, z4)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(fibs_2#1(z2, z3, z4, bot[6]), z0, z1), FIBS_2#1(z2, z3, z4, bot[6])) ZIPWITH_L_F_XS_YS#1(plus, fibs, z0, z1) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(z0, z1, z2), z3, z4) -> c11(COND_ZIPWITH_L_F_XS_YS(fibs_2#1(z0, z1, z2, bot[7]), z3), FIBS_2#1(z0, z1, z2, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, z4) -> c12(COND_ZIPWITH_L_F_XS_YS(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), ZIPWITH_L_F_XS_YS#1(z0, z1, z2, bot[7])) ZIPWITH_L#3(z0, z1) -> c13 MAIN(z0) -> c14(COND_TAKE_L_N_XS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0)) S tuples: FIBS_2#1(zipwith_l, plus, tail_l, z0) -> c(ZIPWITH_L#3(fibs, fibs_2(zipwith_l, plus, tail_l))) COND_TAKE_L_N_XS(ConsL(z0, z1), 0) -> c1 COND_TAKE_L_N_XS(ConsL(z0, fibs_2(z1, z2, z3)), S(z4)) -> c2(COND_TAKE_L_N_XS(fibs_2#1(z1, z2, z3, bot[0]), z4), FIBS_2#1(z1, z2, z3, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(z1, z2, z3)), S(z4)) -> c3(COND_TAKE_L_N_XS(zipwith_l_f_xs_ys#1(z1, z2, z3, bot[0]), z4), ZIPWITH_L_F_XS_YS#1(z1, z2, z3, bot[0])) PLUS#2(0, z0) -> c4 PLUS#2(S(z0), z1) -> c5(PLUS#2(z0, z1)) COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c7(ZIPWITH_L#3(z3, z1)) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(z2, z3, z4)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), z0, z1), ZIPWITH_L_F_XS_YS#1(z2, z3, z4, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), fibs_2(z2, z3, z4)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(fibs_2#1(z2, z3, z4, bot[6]), z0, z1), FIBS_2#1(z2, z3, z4, bot[6])) ZIPWITH_L_F_XS_YS#1(plus, fibs, z0, z1) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(z0, z1, z2), z3, z4) -> c11(COND_ZIPWITH_L_F_XS_YS(fibs_2#1(z0, z1, z2, bot[7]), z3), FIBS_2#1(z0, z1, z2, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, z4) -> c12(COND_ZIPWITH_L_F_XS_YS(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), ZIPWITH_L_F_XS_YS#1(z0, z1, z2, bot[7])) ZIPWITH_L#3(z0, z1) -> c13 MAIN(z0) -> c14(COND_TAKE_L_N_XS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0)) K tuples:none Defined Rule Symbols: fibs_2#1_4, cond_take_l_n_xs_2, plus#2_2, cond_zipwith_l_f_xs_ys_1_3, cond_zipwith_l_f_xs_ys_2, zipwith_l_f_xs_ys#1_4, zipwith_l#3_2, main_1 Defined Pair Symbols: FIBS_2#1_4, COND_TAKE_L_N_XS_2, PLUS#2_2, COND_ZIPWITH_L_F_XS_YS_1_3, COND_ZIPWITH_L_F_XS_YS_2, ZIPWITH_L_F_XS_YS#1_4, ZIPWITH_L#3_2, MAIN_1 Compound Symbols: c_1, c1, c2_2, c3_2, c4, c5_1, c6_1, c7_1, c8_2, c9_2, c10_1, c11_2, c12_2, c13, c14_1 ---------------------------------------- (25) CdtLeafRemovalProof (ComplexityIfPolyImplication) Removed 1 leading nodes: MAIN(z0) -> c14(COND_TAKE_L_N_XS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0)) Removed 5 trailing nodes: ZIPWITH_L#3(z0, z1) -> c13 COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c7(ZIPWITH_L#3(z3, z1)) PLUS#2(0, z0) -> c4 FIBS_2#1(zipwith_l, plus, tail_l, z0) -> c(ZIPWITH_L#3(fibs, fibs_2(zipwith_l, plus, tail_l))) COND_TAKE_L_N_XS(ConsL(z0, z1), 0) -> c1 ---------------------------------------- (26) Obligation: Complexity Dependency Tuples Problem Rules: fibs_2#1(zipwith_l, plus, tail_l, z0) -> ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))) cond_take_l_n_xs(ConsL(z0, z1), 0) -> Nil cond_take_l_n_xs(ConsL(z0, fibs_2(z1, z2, z3)), S(z4)) -> Cons(z0, cond_take_l_n_xs(fibs_2#1(z1, z2, z3, bot[0]), z4)) cond_take_l_n_xs(ConsL(z0, zipwith_l_f_xs_ys(z1, z2, z3)), S(z4)) -> Cons(z0, cond_take_l_n_xs(zipwith_l_f_xs_ys#1(z1, z2, z3, bot[0]), z4)) plus#2(0, z0) -> z0 plus#2(S(z0), z1) -> S(plus#2(z0, z1)) cond_zipwith_l_f_xs_ys_1(ConsL(z0, z1), z2, z3) -> ConsL(plus#2(z2, z0), zipwith_l#3(z3, z1)) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), zipwith_l_f_xs_ys(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), fibs_2(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), z0, z1) zipwith_l_f_xs_ys#1(plus, fibs, z0, z1) -> cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0) zipwith_l_f_xs_ys#1(plus, fibs_2(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3) zipwith_l_f_xs_ys#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3) zipwith_l#3(z0, z1) -> zipwith_l_f_xs_ys(plus, z0, z1) main(z0) -> cond_take_l_n_xs(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0) Tuples: COND_TAKE_L_N_XS(ConsL(z0, fibs_2(z1, z2, z3)), S(z4)) -> c2(COND_TAKE_L_N_XS(fibs_2#1(z1, z2, z3, bot[0]), z4), FIBS_2#1(z1, z2, z3, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(z1, z2, z3)), S(z4)) -> c3(COND_TAKE_L_N_XS(zipwith_l_f_xs_ys#1(z1, z2, z3, bot[0]), z4), ZIPWITH_L_F_XS_YS#1(z1, z2, z3, bot[0])) PLUS#2(S(z0), z1) -> c5(PLUS#2(z0, z1)) COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(z2, z3, z4)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), z0, z1), ZIPWITH_L_F_XS_YS#1(z2, z3, z4, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), fibs_2(z2, z3, z4)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(fibs_2#1(z2, z3, z4, bot[6]), z0, z1), FIBS_2#1(z2, z3, z4, bot[6])) ZIPWITH_L_F_XS_YS#1(plus, fibs, z0, z1) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(z0, z1, z2), z3, z4) -> c11(COND_ZIPWITH_L_F_XS_YS(fibs_2#1(z0, z1, z2, bot[7]), z3), FIBS_2#1(z0, z1, z2, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, z4) -> c12(COND_ZIPWITH_L_F_XS_YS(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), ZIPWITH_L_F_XS_YS#1(z0, z1, z2, bot[7])) S tuples: COND_TAKE_L_N_XS(ConsL(z0, fibs_2(z1, z2, z3)), S(z4)) -> c2(COND_TAKE_L_N_XS(fibs_2#1(z1, z2, z3, bot[0]), z4), FIBS_2#1(z1, z2, z3, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(z1, z2, z3)), S(z4)) -> c3(COND_TAKE_L_N_XS(zipwith_l_f_xs_ys#1(z1, z2, z3, bot[0]), z4), ZIPWITH_L_F_XS_YS#1(z1, z2, z3, bot[0])) PLUS#2(S(z0), z1) -> c5(PLUS#2(z0, z1)) COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(z2, z3, z4)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), z0, z1), ZIPWITH_L_F_XS_YS#1(z2, z3, z4, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), fibs_2(z2, z3, z4)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(fibs_2#1(z2, z3, z4, bot[6]), z0, z1), FIBS_2#1(z2, z3, z4, bot[6])) ZIPWITH_L_F_XS_YS#1(plus, fibs, z0, z1) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(z0, z1, z2), z3, z4) -> c11(COND_ZIPWITH_L_F_XS_YS(fibs_2#1(z0, z1, z2, bot[7]), z3), FIBS_2#1(z0, z1, z2, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, z4) -> c12(COND_ZIPWITH_L_F_XS_YS(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), ZIPWITH_L_F_XS_YS#1(z0, z1, z2, bot[7])) K tuples:none Defined Rule Symbols: fibs_2#1_4, cond_take_l_n_xs_2, plus#2_2, cond_zipwith_l_f_xs_ys_1_3, cond_zipwith_l_f_xs_ys_2, zipwith_l_f_xs_ys#1_4, zipwith_l#3_2, main_1 Defined Pair Symbols: COND_TAKE_L_N_XS_2, PLUS#2_2, COND_ZIPWITH_L_F_XS_YS_1_3, COND_ZIPWITH_L_F_XS_YS_2, ZIPWITH_L_F_XS_YS#1_4 Compound Symbols: c2_2, c3_2, c5_1, c6_1, c8_2, c9_2, c10_1, c11_2, c12_2 ---------------------------------------- (27) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (28) Obligation: Complexity Dependency Tuples Problem Rules: fibs_2#1(zipwith_l, plus, tail_l, z0) -> ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))) cond_take_l_n_xs(ConsL(z0, z1), 0) -> Nil cond_take_l_n_xs(ConsL(z0, fibs_2(z1, z2, z3)), S(z4)) -> Cons(z0, cond_take_l_n_xs(fibs_2#1(z1, z2, z3, bot[0]), z4)) cond_take_l_n_xs(ConsL(z0, zipwith_l_f_xs_ys(z1, z2, z3)), S(z4)) -> Cons(z0, cond_take_l_n_xs(zipwith_l_f_xs_ys#1(z1, z2, z3, bot[0]), z4)) plus#2(0, z0) -> z0 plus#2(S(z0), z1) -> S(plus#2(z0, z1)) cond_zipwith_l_f_xs_ys_1(ConsL(z0, z1), z2, z3) -> ConsL(plus#2(z2, z0), zipwith_l#3(z3, z1)) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), zipwith_l_f_xs_ys(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), fibs_2(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), z0, z1) zipwith_l_f_xs_ys#1(plus, fibs, z0, z1) -> cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0) zipwith_l_f_xs_ys#1(plus, fibs_2(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3) zipwith_l_f_xs_ys#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3) zipwith_l#3(z0, z1) -> zipwith_l_f_xs_ys(plus, z0, z1) main(z0) -> cond_take_l_n_xs(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0) Tuples: COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(z1, z2, z3)), S(z4)) -> c3(COND_TAKE_L_N_XS(zipwith_l_f_xs_ys#1(z1, z2, z3, bot[0]), z4), ZIPWITH_L_F_XS_YS#1(z1, z2, z3, bot[0])) PLUS#2(S(z0), z1) -> c5(PLUS#2(z0, z1)) COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(z2, z3, z4)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), z0, z1), ZIPWITH_L_F_XS_YS#1(z2, z3, z4, bot[6])) ZIPWITH_L_F_XS_YS#1(plus, fibs, z0, z1) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, z4) -> c12(COND_ZIPWITH_L_F_XS_YS(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), ZIPWITH_L_F_XS_YS#1(z0, z1, z2, bot[7])) COND_TAKE_L_N_XS(ConsL(z0, fibs_2(z1, z2, z3)), S(z4)) -> c2(COND_TAKE_L_N_XS(fibs_2#1(z1, z2, z3, bot[0]), z4)) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), fibs_2(z2, z3, z4)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(fibs_2#1(z2, z3, z4, bot[6]), z0, z1)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(z0, z1, z2), z3, z4) -> c11(COND_ZIPWITH_L_F_XS_YS(fibs_2#1(z0, z1, z2, bot[7]), z3)) S tuples: COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(z1, z2, z3)), S(z4)) -> c3(COND_TAKE_L_N_XS(zipwith_l_f_xs_ys#1(z1, z2, z3, bot[0]), z4), ZIPWITH_L_F_XS_YS#1(z1, z2, z3, bot[0])) PLUS#2(S(z0), z1) -> c5(PLUS#2(z0, z1)) COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(z2, z3, z4)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), z0, z1), ZIPWITH_L_F_XS_YS#1(z2, z3, z4, bot[6])) ZIPWITH_L_F_XS_YS#1(plus, fibs, z0, z1) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, z4) -> c12(COND_ZIPWITH_L_F_XS_YS(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), ZIPWITH_L_F_XS_YS#1(z0, z1, z2, bot[7])) COND_TAKE_L_N_XS(ConsL(z0, fibs_2(z1, z2, z3)), S(z4)) -> c2(COND_TAKE_L_N_XS(fibs_2#1(z1, z2, z3, bot[0]), z4)) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), fibs_2(z2, z3, z4)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(fibs_2#1(z2, z3, z4, bot[6]), z0, z1)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(z0, z1, z2), z3, z4) -> c11(COND_ZIPWITH_L_F_XS_YS(fibs_2#1(z0, z1, z2, bot[7]), z3)) K tuples:none Defined Rule Symbols: fibs_2#1_4, cond_take_l_n_xs_2, plus#2_2, cond_zipwith_l_f_xs_ys_1_3, cond_zipwith_l_f_xs_ys_2, zipwith_l_f_xs_ys#1_4, zipwith_l#3_2, main_1 Defined Pair Symbols: COND_TAKE_L_N_XS_2, PLUS#2_2, COND_ZIPWITH_L_F_XS_YS_1_3, COND_ZIPWITH_L_F_XS_YS_2, ZIPWITH_L_F_XS_YS#1_4 Compound Symbols: c3_2, c5_1, c6_1, c8_2, c10_1, c12_2, c2_1, c9_1, c11_1 ---------------------------------------- (29) CdtUsableRulesProof (BOTH BOUNDS(ID, ID)) The following rules are not usable and were removed: cond_take_l_n_xs(ConsL(z0, z1), 0) -> Nil cond_take_l_n_xs(ConsL(z0, fibs_2(z1, z2, z3)), S(z4)) -> Cons(z0, cond_take_l_n_xs(fibs_2#1(z1, z2, z3, bot[0]), z4)) cond_take_l_n_xs(ConsL(z0, zipwith_l_f_xs_ys(z1, z2, z3)), S(z4)) -> Cons(z0, cond_take_l_n_xs(zipwith_l_f_xs_ys#1(z1, z2, z3, bot[0]), z4)) main(z0) -> cond_take_l_n_xs(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0) ---------------------------------------- (30) Obligation: Complexity Dependency Tuples Problem Rules: zipwith_l_f_xs_ys#1(plus, fibs, z0, z1) -> cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0) zipwith_l_f_xs_ys#1(plus, fibs_2(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3) zipwith_l_f_xs_ys#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), zipwith_l_f_xs_ys(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), fibs_2(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys_1(ConsL(z0, z1), z2, z3) -> ConsL(plus#2(z2, z0), zipwith_l#3(z3, z1)) fibs_2#1(zipwith_l, plus, tail_l, z0) -> ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))) zipwith_l#3(z0, z1) -> zipwith_l_f_xs_ys(plus, z0, z1) plus#2(0, z0) -> z0 plus#2(S(z0), z1) -> S(plus#2(z0, z1)) Tuples: COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(z1, z2, z3)), S(z4)) -> c3(COND_TAKE_L_N_XS(zipwith_l_f_xs_ys#1(z1, z2, z3, bot[0]), z4), ZIPWITH_L_F_XS_YS#1(z1, z2, z3, bot[0])) PLUS#2(S(z0), z1) -> c5(PLUS#2(z0, z1)) COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(z2, z3, z4)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), z0, z1), ZIPWITH_L_F_XS_YS#1(z2, z3, z4, bot[6])) ZIPWITH_L_F_XS_YS#1(plus, fibs, z0, z1) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, z4) -> c12(COND_ZIPWITH_L_F_XS_YS(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), ZIPWITH_L_F_XS_YS#1(z0, z1, z2, bot[7])) COND_TAKE_L_N_XS(ConsL(z0, fibs_2(z1, z2, z3)), S(z4)) -> c2(COND_TAKE_L_N_XS(fibs_2#1(z1, z2, z3, bot[0]), z4)) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), fibs_2(z2, z3, z4)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(fibs_2#1(z2, z3, z4, bot[6]), z0, z1)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(z0, z1, z2), z3, z4) -> c11(COND_ZIPWITH_L_F_XS_YS(fibs_2#1(z0, z1, z2, bot[7]), z3)) S tuples: COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(z1, z2, z3)), S(z4)) -> c3(COND_TAKE_L_N_XS(zipwith_l_f_xs_ys#1(z1, z2, z3, bot[0]), z4), ZIPWITH_L_F_XS_YS#1(z1, z2, z3, bot[0])) PLUS#2(S(z0), z1) -> c5(PLUS#2(z0, z1)) COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(z2, z3, z4)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), z0, z1), ZIPWITH_L_F_XS_YS#1(z2, z3, z4, bot[6])) ZIPWITH_L_F_XS_YS#1(plus, fibs, z0, z1) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, z4) -> c12(COND_ZIPWITH_L_F_XS_YS(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), ZIPWITH_L_F_XS_YS#1(z0, z1, z2, bot[7])) COND_TAKE_L_N_XS(ConsL(z0, fibs_2(z1, z2, z3)), S(z4)) -> c2(COND_TAKE_L_N_XS(fibs_2#1(z1, z2, z3, bot[0]), z4)) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), fibs_2(z2, z3, z4)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(fibs_2#1(z2, z3, z4, bot[6]), z0, z1)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(z0, z1, z2), z3, z4) -> c11(COND_ZIPWITH_L_F_XS_YS(fibs_2#1(z0, z1, z2, bot[7]), z3)) K tuples:none Defined Rule Symbols: zipwith_l_f_xs_ys#1_4, cond_zipwith_l_f_xs_ys_2, cond_zipwith_l_f_xs_ys_1_3, fibs_2#1_4, zipwith_l#3_2, plus#2_2 Defined Pair Symbols: COND_TAKE_L_N_XS_2, PLUS#2_2, COND_ZIPWITH_L_F_XS_YS_1_3, COND_ZIPWITH_L_F_XS_YS_2, ZIPWITH_L_F_XS_YS#1_4 Compound Symbols: c3_2, c5_1, c6_1, c8_2, c10_1, c12_2, c2_1, c9_1, c11_1 ---------------------------------------- (31) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1))) Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S. COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(z1, z2, z3)), S(z4)) -> c3(COND_TAKE_L_N_XS(zipwith_l_f_xs_ys#1(z1, z2, z3, bot[0]), z4), ZIPWITH_L_F_XS_YS#1(z1, z2, z3, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, fibs_2(z1, z2, z3)), S(z4)) -> c2(COND_TAKE_L_N_XS(fibs_2#1(z1, z2, z3, bot[0]), z4)) We considered the (Usable) Rules:none And the Tuples: COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(z1, z2, z3)), S(z4)) -> c3(COND_TAKE_L_N_XS(zipwith_l_f_xs_ys#1(z1, z2, z3, bot[0]), z4), ZIPWITH_L_F_XS_YS#1(z1, z2, z3, bot[0])) PLUS#2(S(z0), z1) -> c5(PLUS#2(z0, z1)) COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(z2, z3, z4)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), z0, z1), ZIPWITH_L_F_XS_YS#1(z2, z3, z4, bot[6])) ZIPWITH_L_F_XS_YS#1(plus, fibs, z0, z1) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, z4) -> c12(COND_ZIPWITH_L_F_XS_YS(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), ZIPWITH_L_F_XS_YS#1(z0, z1, z2, bot[7])) COND_TAKE_L_N_XS(ConsL(z0, fibs_2(z1, z2, z3)), S(z4)) -> c2(COND_TAKE_L_N_XS(fibs_2#1(z1, z2, z3, bot[0]), z4)) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), fibs_2(z2, z3, z4)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(fibs_2#1(z2, z3, z4, bot[6]), z0, z1)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(z0, z1, z2), z3, z4) -> c11(COND_ZIPWITH_L_F_XS_YS(fibs_2#1(z0, z1, z2, bot[7]), z3)) The order we found is given by the following interpretation: Polynomial interpretation : POL(0) = 0 POL(COND_TAKE_L_N_XS(x_1, x_2)) = x_2 POL(COND_ZIPWITH_L_F_XS_YS(x_1, x_2)) = 0 POL(COND_ZIPWITH_L_F_XS_YS_1(x_1, x_2, x_3)) = 0 POL(ConsL(x_1, x_2)) = 0 POL(PLUS#2(x_1, x_2)) = 0 POL(S(x_1)) = [1] + x_1 POL(ZIPWITH_L_F_XS_YS#1(x_1, x_2, x_3, x_4)) = x_4 POL(bot[0]) = 0 POL(bot[6]) = 0 POL(bot[7]) = 0 POL(c10(x_1)) = x_1 POL(c11(x_1)) = x_1 POL(c12(x_1, x_2)) = x_1 + x_2 POL(c2(x_1)) = x_1 POL(c3(x_1, x_2)) = x_1 + x_2 POL(c5(x_1)) = x_1 POL(c6(x_1)) = x_1 POL(c8(x_1, x_2)) = x_1 + x_2 POL(c9(x_1)) = x_1 POL(cond_zipwith_l_f_xs_ys(x_1, x_2)) = [1] POL(cond_zipwith_l_f_xs_ys_1(x_1, x_2, x_3)) = [1] + x_1 + x_2 + x_3 POL(fibs) = [1] POL(fibs_2(x_1, x_2, x_3)) = 0 POL(fibs_2#1(x_1, x_2, x_3, x_4)) = x_1 + x_2 + x_3 POL(plus) = 0 POL(plus#2(x_1, x_2)) = [1] + x_1 + x_2 POL(tail_l) = 0 POL(zipwith_l) = 0 POL(zipwith_l#3(x_1, x_2)) = [1] + x_1 + x_2 POL(zipwith_l_f_xs_ys(x_1, x_2, x_3)) = x_1 POL(zipwith_l_f_xs_ys#1(x_1, x_2, x_3, x_4)) = x_1 + x_2 + x_3 ---------------------------------------- (32) Obligation: Complexity Dependency Tuples Problem Rules: zipwith_l_f_xs_ys#1(plus, fibs, z0, z1) -> cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0) zipwith_l_f_xs_ys#1(plus, fibs_2(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3) zipwith_l_f_xs_ys#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), zipwith_l_f_xs_ys(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), fibs_2(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys_1(ConsL(z0, z1), z2, z3) -> ConsL(plus#2(z2, z0), zipwith_l#3(z3, z1)) fibs_2#1(zipwith_l, plus, tail_l, z0) -> ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))) zipwith_l#3(z0, z1) -> zipwith_l_f_xs_ys(plus, z0, z1) plus#2(0, z0) -> z0 plus#2(S(z0), z1) -> S(plus#2(z0, z1)) Tuples: COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(z1, z2, z3)), S(z4)) -> c3(COND_TAKE_L_N_XS(zipwith_l_f_xs_ys#1(z1, z2, z3, bot[0]), z4), ZIPWITH_L_F_XS_YS#1(z1, z2, z3, bot[0])) PLUS#2(S(z0), z1) -> c5(PLUS#2(z0, z1)) COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(z2, z3, z4)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), z0, z1), ZIPWITH_L_F_XS_YS#1(z2, z3, z4, bot[6])) ZIPWITH_L_F_XS_YS#1(plus, fibs, z0, z1) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, z4) -> c12(COND_ZIPWITH_L_F_XS_YS(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), ZIPWITH_L_F_XS_YS#1(z0, z1, z2, bot[7])) COND_TAKE_L_N_XS(ConsL(z0, fibs_2(z1, z2, z3)), S(z4)) -> c2(COND_TAKE_L_N_XS(fibs_2#1(z1, z2, z3, bot[0]), z4)) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), fibs_2(z2, z3, z4)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(fibs_2#1(z2, z3, z4, bot[6]), z0, z1)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(z0, z1, z2), z3, z4) -> c11(COND_ZIPWITH_L_F_XS_YS(fibs_2#1(z0, z1, z2, bot[7]), z3)) S tuples: PLUS#2(S(z0), z1) -> c5(PLUS#2(z0, z1)) COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(z2, z3, z4)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), z0, z1), ZIPWITH_L_F_XS_YS#1(z2, z3, z4, bot[6])) ZIPWITH_L_F_XS_YS#1(plus, fibs, z0, z1) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, z4) -> c12(COND_ZIPWITH_L_F_XS_YS(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), ZIPWITH_L_F_XS_YS#1(z0, z1, z2, bot[7])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), fibs_2(z2, z3, z4)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(fibs_2#1(z2, z3, z4, bot[6]), z0, z1)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(z0, z1, z2), z3, z4) -> c11(COND_ZIPWITH_L_F_XS_YS(fibs_2#1(z0, z1, z2, bot[7]), z3)) K tuples: COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(z1, z2, z3)), S(z4)) -> c3(COND_TAKE_L_N_XS(zipwith_l_f_xs_ys#1(z1, z2, z3, bot[0]), z4), ZIPWITH_L_F_XS_YS#1(z1, z2, z3, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, fibs_2(z1, z2, z3)), S(z4)) -> c2(COND_TAKE_L_N_XS(fibs_2#1(z1, z2, z3, bot[0]), z4)) Defined Rule Symbols: zipwith_l_f_xs_ys#1_4, cond_zipwith_l_f_xs_ys_2, cond_zipwith_l_f_xs_ys_1_3, fibs_2#1_4, zipwith_l#3_2, plus#2_2 Defined Pair Symbols: COND_TAKE_L_N_XS_2, PLUS#2_2, COND_ZIPWITH_L_F_XS_YS_1_3, COND_ZIPWITH_L_F_XS_YS_2, ZIPWITH_L_F_XS_YS#1_4 Compound Symbols: c3_2, c5_1, c6_1, c8_2, c10_1, c12_2, c2_1, c9_1, c11_1 ---------------------------------------- (33) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(z1, z2, z3)), S(z4)) -> c3(COND_TAKE_L_N_XS(zipwith_l_f_xs_ys#1(z1, z2, z3, bot[0]), z4), ZIPWITH_L_F_XS_YS#1(z1, z2, z3, bot[0])) by COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, z0)), S(x4)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x4), ZIPWITH_L_F_XS_YS#1(plus, fibs, z0, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3)), S(x4)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x4), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(z0, z1, z2), z3, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3)), S(x4)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, bot[0])) ---------------------------------------- (34) Obligation: Complexity Dependency Tuples Problem Rules: zipwith_l_f_xs_ys#1(plus, fibs, z0, z1) -> cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0) zipwith_l_f_xs_ys#1(plus, fibs_2(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3) zipwith_l_f_xs_ys#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), zipwith_l_f_xs_ys(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), fibs_2(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys_1(ConsL(z0, z1), z2, z3) -> ConsL(plus#2(z2, z0), zipwith_l#3(z3, z1)) fibs_2#1(zipwith_l, plus, tail_l, z0) -> ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))) zipwith_l#3(z0, z1) -> zipwith_l_f_xs_ys(plus, z0, z1) plus#2(0, z0) -> z0 plus#2(S(z0), z1) -> S(plus#2(z0, z1)) Tuples: PLUS#2(S(z0), z1) -> c5(PLUS#2(z0, z1)) COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(z2, z3, z4)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), z0, z1), ZIPWITH_L_F_XS_YS#1(z2, z3, z4, bot[6])) ZIPWITH_L_F_XS_YS#1(plus, fibs, z0, z1) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, z4) -> c12(COND_ZIPWITH_L_F_XS_YS(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), ZIPWITH_L_F_XS_YS#1(z0, z1, z2, bot[7])) COND_TAKE_L_N_XS(ConsL(z0, fibs_2(z1, z2, z3)), S(z4)) -> c2(COND_TAKE_L_N_XS(fibs_2#1(z1, z2, z3, bot[0]), z4)) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), fibs_2(z2, z3, z4)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(fibs_2#1(z2, z3, z4, bot[6]), z0, z1)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(z0, z1, z2), z3, z4) -> c11(COND_ZIPWITH_L_F_XS_YS(fibs_2#1(z0, z1, z2, bot[7]), z3)) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, z0)), S(x4)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x4), ZIPWITH_L_F_XS_YS#1(plus, fibs, z0, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3)), S(x4)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x4), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(z0, z1, z2), z3, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3)), S(x4)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, bot[0])) S tuples: PLUS#2(S(z0), z1) -> c5(PLUS#2(z0, z1)) COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(z2, z3, z4)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), z0, z1), ZIPWITH_L_F_XS_YS#1(z2, z3, z4, bot[6])) ZIPWITH_L_F_XS_YS#1(plus, fibs, z0, z1) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, z4) -> c12(COND_ZIPWITH_L_F_XS_YS(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), ZIPWITH_L_F_XS_YS#1(z0, z1, z2, bot[7])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), fibs_2(z2, z3, z4)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(fibs_2#1(z2, z3, z4, bot[6]), z0, z1)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(z0, z1, z2), z3, z4) -> c11(COND_ZIPWITH_L_F_XS_YS(fibs_2#1(z0, z1, z2, bot[7]), z3)) K tuples: COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(z1, z2, z3)), S(z4)) -> c3(COND_TAKE_L_N_XS(zipwith_l_f_xs_ys#1(z1, z2, z3, bot[0]), z4), ZIPWITH_L_F_XS_YS#1(z1, z2, z3, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, fibs_2(z1, z2, z3)), S(z4)) -> c2(COND_TAKE_L_N_XS(fibs_2#1(z1, z2, z3, bot[0]), z4)) Defined Rule Symbols: zipwith_l_f_xs_ys#1_4, cond_zipwith_l_f_xs_ys_2, cond_zipwith_l_f_xs_ys_1_3, fibs_2#1_4, zipwith_l#3_2, plus#2_2 Defined Pair Symbols: PLUS#2_2, COND_ZIPWITH_L_F_XS_YS_1_3, COND_ZIPWITH_L_F_XS_YS_2, ZIPWITH_L_F_XS_YS#1_4, COND_TAKE_L_N_XS_2 Compound Symbols: c5_1, c6_1, c8_2, c10_1, c12_2, c2_1, c9_1, c11_1, c3_2 ---------------------------------------- (35) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(z2, z3, z4)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), z0, z1), ZIPWITH_L_F_XS_YS#1(z2, z3, z4, bot[6])) by COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, z0)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, z0, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(z0, z1, z2), z3, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, bot[6])) ---------------------------------------- (36) Obligation: Complexity Dependency Tuples Problem Rules: zipwith_l_f_xs_ys#1(plus, fibs, z0, z1) -> cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0) zipwith_l_f_xs_ys#1(plus, fibs_2(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3) zipwith_l_f_xs_ys#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), zipwith_l_f_xs_ys(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), fibs_2(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys_1(ConsL(z0, z1), z2, z3) -> ConsL(plus#2(z2, z0), zipwith_l#3(z3, z1)) fibs_2#1(zipwith_l, plus, tail_l, z0) -> ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))) zipwith_l#3(z0, z1) -> zipwith_l_f_xs_ys(plus, z0, z1) plus#2(0, z0) -> z0 plus#2(S(z0), z1) -> S(plus#2(z0, z1)) Tuples: PLUS#2(S(z0), z1) -> c5(PLUS#2(z0, z1)) COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) ZIPWITH_L_F_XS_YS#1(plus, fibs, z0, z1) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, z4) -> c12(COND_ZIPWITH_L_F_XS_YS(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), ZIPWITH_L_F_XS_YS#1(z0, z1, z2, bot[7])) COND_TAKE_L_N_XS(ConsL(z0, fibs_2(z1, z2, z3)), S(z4)) -> c2(COND_TAKE_L_N_XS(fibs_2#1(z1, z2, z3, bot[0]), z4)) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), fibs_2(z2, z3, z4)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(fibs_2#1(z2, z3, z4, bot[6]), z0, z1)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(z0, z1, z2), z3, z4) -> c11(COND_ZIPWITH_L_F_XS_YS(fibs_2#1(z0, z1, z2, bot[7]), z3)) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, z0)), S(x4)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x4), ZIPWITH_L_F_XS_YS#1(plus, fibs, z0, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3)), S(x4)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x4), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(z0, z1, z2), z3, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3)), S(x4)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, z0)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, z0, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(z0, z1, z2), z3, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, bot[6])) S tuples: PLUS#2(S(z0), z1) -> c5(PLUS#2(z0, z1)) COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) ZIPWITH_L_F_XS_YS#1(plus, fibs, z0, z1) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, z4) -> c12(COND_ZIPWITH_L_F_XS_YS(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), ZIPWITH_L_F_XS_YS#1(z0, z1, z2, bot[7])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), fibs_2(z2, z3, z4)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(fibs_2#1(z2, z3, z4, bot[6]), z0, z1)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(z0, z1, z2), z3, z4) -> c11(COND_ZIPWITH_L_F_XS_YS(fibs_2#1(z0, z1, z2, bot[7]), z3)) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, z0)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, z0, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(z0, z1, z2), z3, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, bot[6])) K tuples: COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(z1, z2, z3)), S(z4)) -> c3(COND_TAKE_L_N_XS(zipwith_l_f_xs_ys#1(z1, z2, z3, bot[0]), z4), ZIPWITH_L_F_XS_YS#1(z1, z2, z3, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, fibs_2(z1, z2, z3)), S(z4)) -> c2(COND_TAKE_L_N_XS(fibs_2#1(z1, z2, z3, bot[0]), z4)) Defined Rule Symbols: zipwith_l_f_xs_ys#1_4, cond_zipwith_l_f_xs_ys_2, cond_zipwith_l_f_xs_ys_1_3, fibs_2#1_4, zipwith_l#3_2, plus#2_2 Defined Pair Symbols: PLUS#2_2, COND_ZIPWITH_L_F_XS_YS_1_3, ZIPWITH_L_F_XS_YS#1_4, COND_TAKE_L_N_XS_2, COND_ZIPWITH_L_F_XS_YS_2 Compound Symbols: c5_1, c6_1, c10_1, c12_2, c2_1, c9_1, c11_1, c3_2, c8_2 ---------------------------------------- (37) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, z4) -> c12(COND_ZIPWITH_L_F_XS_YS(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), ZIPWITH_L_F_XS_YS#1(z0, z1, z2, bot[7])) by ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3, x4) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, z0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3, x4) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(z0, z1, z2), z3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3, x4) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x3), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, bot[7])) ---------------------------------------- (38) Obligation: Complexity Dependency Tuples Problem Rules: zipwith_l_f_xs_ys#1(plus, fibs, z0, z1) -> cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0) zipwith_l_f_xs_ys#1(plus, fibs_2(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3) zipwith_l_f_xs_ys#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), zipwith_l_f_xs_ys(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), fibs_2(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys_1(ConsL(z0, z1), z2, z3) -> ConsL(plus#2(z2, z0), zipwith_l#3(z3, z1)) fibs_2#1(zipwith_l, plus, tail_l, z0) -> ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))) zipwith_l#3(z0, z1) -> zipwith_l_f_xs_ys(plus, z0, z1) plus#2(0, z0) -> z0 plus#2(S(z0), z1) -> S(plus#2(z0, z1)) Tuples: PLUS#2(S(z0), z1) -> c5(PLUS#2(z0, z1)) COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) ZIPWITH_L_F_XS_YS#1(plus, fibs, z0, z1) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0)) COND_TAKE_L_N_XS(ConsL(z0, fibs_2(z1, z2, z3)), S(z4)) -> c2(COND_TAKE_L_N_XS(fibs_2#1(z1, z2, z3, bot[0]), z4)) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), fibs_2(z2, z3, z4)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(fibs_2#1(z2, z3, z4, bot[6]), z0, z1)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(z0, z1, z2), z3, z4) -> c11(COND_ZIPWITH_L_F_XS_YS(fibs_2#1(z0, z1, z2, bot[7]), z3)) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, z0)), S(x4)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x4), ZIPWITH_L_F_XS_YS#1(plus, fibs, z0, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3)), S(x4)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x4), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(z0, z1, z2), z3, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3)), S(x4)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, z0)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, z0, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(z0, z1, z2), z3, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, bot[6])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3, x4) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, z0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3, x4) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(z0, z1, z2), z3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3, x4) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x3), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, bot[7])) S tuples: PLUS#2(S(z0), z1) -> c5(PLUS#2(z0, z1)) COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) ZIPWITH_L_F_XS_YS#1(plus, fibs, z0, z1) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0)) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), fibs_2(z2, z3, z4)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(fibs_2#1(z2, z3, z4, bot[6]), z0, z1)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(z0, z1, z2), z3, z4) -> c11(COND_ZIPWITH_L_F_XS_YS(fibs_2#1(z0, z1, z2, bot[7]), z3)) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, z0)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, z0, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(z0, z1, z2), z3, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, bot[6])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3, x4) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, z0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3, x4) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(z0, z1, z2), z3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3, x4) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x3), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, bot[7])) K tuples: COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(z1, z2, z3)), S(z4)) -> c3(COND_TAKE_L_N_XS(zipwith_l_f_xs_ys#1(z1, z2, z3, bot[0]), z4), ZIPWITH_L_F_XS_YS#1(z1, z2, z3, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, fibs_2(z1, z2, z3)), S(z4)) -> c2(COND_TAKE_L_N_XS(fibs_2#1(z1, z2, z3, bot[0]), z4)) Defined Rule Symbols: zipwith_l_f_xs_ys#1_4, cond_zipwith_l_f_xs_ys_2, cond_zipwith_l_f_xs_ys_1_3, fibs_2#1_4, zipwith_l#3_2, plus#2_2 Defined Pair Symbols: PLUS#2_2, COND_ZIPWITH_L_F_XS_YS_1_3, ZIPWITH_L_F_XS_YS#1_4, COND_TAKE_L_N_XS_2, COND_ZIPWITH_L_F_XS_YS_2 Compound Symbols: c5_1, c6_1, c10_1, c2_1, c9_1, c11_1, c3_2, c8_2, c12_2 ---------------------------------------- (39) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace COND_TAKE_L_N_XS(ConsL(z0, fibs_2(z1, z2, z3)), S(z4)) -> c2(COND_TAKE_L_N_XS(fibs_2#1(z1, z2, z3, bot[0]), z4)) by COND_TAKE_L_N_XS(ConsL(x0, fibs_2(zipwith_l, plus, tail_l)), S(x4)) -> c2(COND_TAKE_L_N_XS(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x4)) ---------------------------------------- (40) Obligation: Complexity Dependency Tuples Problem Rules: zipwith_l_f_xs_ys#1(plus, fibs, z0, z1) -> cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0) zipwith_l_f_xs_ys#1(plus, fibs_2(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3) zipwith_l_f_xs_ys#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), zipwith_l_f_xs_ys(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), fibs_2(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys_1(ConsL(z0, z1), z2, z3) -> ConsL(plus#2(z2, z0), zipwith_l#3(z3, z1)) fibs_2#1(zipwith_l, plus, tail_l, z0) -> ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))) zipwith_l#3(z0, z1) -> zipwith_l_f_xs_ys(plus, z0, z1) plus#2(0, z0) -> z0 plus#2(S(z0), z1) -> S(plus#2(z0, z1)) Tuples: PLUS#2(S(z0), z1) -> c5(PLUS#2(z0, z1)) COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) ZIPWITH_L_F_XS_YS#1(plus, fibs, z0, z1) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0)) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), fibs_2(z2, z3, z4)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(fibs_2#1(z2, z3, z4, bot[6]), z0, z1)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(z0, z1, z2), z3, z4) -> c11(COND_ZIPWITH_L_F_XS_YS(fibs_2#1(z0, z1, z2, bot[7]), z3)) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, z0)), S(x4)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x4), ZIPWITH_L_F_XS_YS#1(plus, fibs, z0, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3)), S(x4)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x4), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(z0, z1, z2), z3, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3)), S(x4)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, z0)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, z0, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(z0, z1, z2), z3, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, bot[6])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3, x4) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, z0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3, x4) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(z0, z1, z2), z3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3, x4) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x3), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, bot[7])) COND_TAKE_L_N_XS(ConsL(x0, fibs_2(zipwith_l, plus, tail_l)), S(x4)) -> c2(COND_TAKE_L_N_XS(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x4)) S tuples: PLUS#2(S(z0), z1) -> c5(PLUS#2(z0, z1)) COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) ZIPWITH_L_F_XS_YS#1(plus, fibs, z0, z1) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0)) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), fibs_2(z2, z3, z4)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(fibs_2#1(z2, z3, z4, bot[6]), z0, z1)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(z0, z1, z2), z3, z4) -> c11(COND_ZIPWITH_L_F_XS_YS(fibs_2#1(z0, z1, z2, bot[7]), z3)) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, z0)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, z0, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(z0, z1, z2), z3, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, bot[6])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3, x4) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, z0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3, x4) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(z0, z1, z2), z3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3, x4) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x3), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, bot[7])) K tuples: COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(z1, z2, z3)), S(z4)) -> c3(COND_TAKE_L_N_XS(zipwith_l_f_xs_ys#1(z1, z2, z3, bot[0]), z4), ZIPWITH_L_F_XS_YS#1(z1, z2, z3, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, fibs_2(z1, z2, z3)), S(z4)) -> c2(COND_TAKE_L_N_XS(fibs_2#1(z1, z2, z3, bot[0]), z4)) Defined Rule Symbols: zipwith_l_f_xs_ys#1_4, cond_zipwith_l_f_xs_ys_2, cond_zipwith_l_f_xs_ys_1_3, fibs_2#1_4, zipwith_l#3_2, plus#2_2 Defined Pair Symbols: PLUS#2_2, COND_ZIPWITH_L_F_XS_YS_1_3, ZIPWITH_L_F_XS_YS#1_4, COND_ZIPWITH_L_F_XS_YS_2, COND_TAKE_L_N_XS_2 Compound Symbols: c5_1, c6_1, c10_1, c9_1, c11_1, c3_2, c8_2, c12_2, c2_1 ---------------------------------------- (41) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), fibs_2(z2, z3, z4)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(fibs_2#1(z2, z3, z4, bot[6]), z0, z1)) by COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x0, x1)) ---------------------------------------- (42) Obligation: Complexity Dependency Tuples Problem Rules: zipwith_l_f_xs_ys#1(plus, fibs, z0, z1) -> cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0) zipwith_l_f_xs_ys#1(plus, fibs_2(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3) zipwith_l_f_xs_ys#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), zipwith_l_f_xs_ys(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), fibs_2(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys_1(ConsL(z0, z1), z2, z3) -> ConsL(plus#2(z2, z0), zipwith_l#3(z3, z1)) fibs_2#1(zipwith_l, plus, tail_l, z0) -> ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))) zipwith_l#3(z0, z1) -> zipwith_l_f_xs_ys(plus, z0, z1) plus#2(0, z0) -> z0 plus#2(S(z0), z1) -> S(plus#2(z0, z1)) Tuples: PLUS#2(S(z0), z1) -> c5(PLUS#2(z0, z1)) COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) ZIPWITH_L_F_XS_YS#1(plus, fibs, z0, z1) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(z0, z1, z2), z3, z4) -> c11(COND_ZIPWITH_L_F_XS_YS(fibs_2#1(z0, z1, z2, bot[7]), z3)) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, z0)), S(x4)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x4), ZIPWITH_L_F_XS_YS#1(plus, fibs, z0, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3)), S(x4)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x4), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(z0, z1, z2), z3, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3)), S(x4)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, z0)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, z0, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(z0, z1, z2), z3, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, bot[6])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3, x4) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, z0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3, x4) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(z0, z1, z2), z3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3, x4) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x3), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, bot[7])) COND_TAKE_L_N_XS(ConsL(x0, fibs_2(zipwith_l, plus, tail_l)), S(x4)) -> c2(COND_TAKE_L_N_XS(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x4)) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x0, x1)) S tuples: PLUS#2(S(z0), z1) -> c5(PLUS#2(z0, z1)) COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) ZIPWITH_L_F_XS_YS#1(plus, fibs, z0, z1) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(z0, z1, z2), z3, z4) -> c11(COND_ZIPWITH_L_F_XS_YS(fibs_2#1(z0, z1, z2, bot[7]), z3)) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, z0)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, z0, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(z0, z1, z2), z3, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, bot[6])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3, x4) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, z0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3, x4) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(z0, z1, z2), z3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3, x4) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x3), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, bot[7])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x0, x1)) K tuples: COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(z1, z2, z3)), S(z4)) -> c3(COND_TAKE_L_N_XS(zipwith_l_f_xs_ys#1(z1, z2, z3, bot[0]), z4), ZIPWITH_L_F_XS_YS#1(z1, z2, z3, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, fibs_2(z1, z2, z3)), S(z4)) -> c2(COND_TAKE_L_N_XS(fibs_2#1(z1, z2, z3, bot[0]), z4)) Defined Rule Symbols: zipwith_l_f_xs_ys#1_4, cond_zipwith_l_f_xs_ys_2, cond_zipwith_l_f_xs_ys_1_3, fibs_2#1_4, zipwith_l#3_2, plus#2_2 Defined Pair Symbols: PLUS#2_2, COND_ZIPWITH_L_F_XS_YS_1_3, ZIPWITH_L_F_XS_YS#1_4, COND_TAKE_L_N_XS_2, COND_ZIPWITH_L_F_XS_YS_2 Compound Symbols: c5_1, c6_1, c10_1, c11_1, c3_2, c8_2, c12_2, c2_1, c9_1 ---------------------------------------- (43) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ZIPWITH_L_F_XS_YS#1(plus, fibs_2(z0, z1, z2), z3, z4) -> c11(COND_ZIPWITH_L_F_XS_YS(fibs_2#1(z0, z1, z2, bot[7]), z3)) by ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, x4) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3)) ---------------------------------------- (44) Obligation: Complexity Dependency Tuples Problem Rules: zipwith_l_f_xs_ys#1(plus, fibs, z0, z1) -> cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0) zipwith_l_f_xs_ys#1(plus, fibs_2(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3) zipwith_l_f_xs_ys#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), zipwith_l_f_xs_ys(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), fibs_2(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys_1(ConsL(z0, z1), z2, z3) -> ConsL(plus#2(z2, z0), zipwith_l#3(z3, z1)) fibs_2#1(zipwith_l, plus, tail_l, z0) -> ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))) zipwith_l#3(z0, z1) -> zipwith_l_f_xs_ys(plus, z0, z1) plus#2(0, z0) -> z0 plus#2(S(z0), z1) -> S(plus#2(z0, z1)) Tuples: PLUS#2(S(z0), z1) -> c5(PLUS#2(z0, z1)) COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) ZIPWITH_L_F_XS_YS#1(plus, fibs, z0, z1) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0)) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, z0)), S(x4)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x4), ZIPWITH_L_F_XS_YS#1(plus, fibs, z0, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3)), S(x4)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x4), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(z0, z1, z2), z3, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3)), S(x4)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, z0)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, z0, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(z0, z1, z2), z3, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, bot[6])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3, x4) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, z0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3, x4) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(z0, z1, z2), z3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3, x4) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x3), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, bot[7])) COND_TAKE_L_N_XS(ConsL(x0, fibs_2(zipwith_l, plus, tail_l)), S(x4)) -> c2(COND_TAKE_L_N_XS(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x4)) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x0, x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, x4) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3)) S tuples: PLUS#2(S(z0), z1) -> c5(PLUS#2(z0, z1)) COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) ZIPWITH_L_F_XS_YS#1(plus, fibs, z0, z1) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0)) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, z0)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, z0, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(z0, z1, z2), z3, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, bot[6])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3, x4) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, z0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3, x4) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(z0, z1, z2), z3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3, x4) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x3), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, bot[7])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x0, x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, x4) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3)) K tuples: COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(z1, z2, z3)), S(z4)) -> c3(COND_TAKE_L_N_XS(zipwith_l_f_xs_ys#1(z1, z2, z3, bot[0]), z4), ZIPWITH_L_F_XS_YS#1(z1, z2, z3, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, fibs_2(z1, z2, z3)), S(z4)) -> c2(COND_TAKE_L_N_XS(fibs_2#1(z1, z2, z3, bot[0]), z4)) Defined Rule Symbols: zipwith_l_f_xs_ys#1_4, cond_zipwith_l_f_xs_ys_2, cond_zipwith_l_f_xs_ys_1_3, fibs_2#1_4, zipwith_l#3_2, plus#2_2 Defined Pair Symbols: PLUS#2_2, COND_ZIPWITH_L_F_XS_YS_1_3, ZIPWITH_L_F_XS_YS#1_4, COND_TAKE_L_N_XS_2, COND_ZIPWITH_L_F_XS_YS_2 Compound Symbols: c5_1, c6_1, c10_1, c3_2, c8_2, c12_2, c2_1, c9_1, c11_1 ---------------------------------------- (45) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, z0)), S(x4)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x4), ZIPWITH_L_F_XS_YS#1(plus, fibs, z0, bot[0])) by COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, x1)), S(x2)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0])) ---------------------------------------- (46) Obligation: Complexity Dependency Tuples Problem Rules: zipwith_l_f_xs_ys#1(plus, fibs, z0, z1) -> cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0) zipwith_l_f_xs_ys#1(plus, fibs_2(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3) zipwith_l_f_xs_ys#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), zipwith_l_f_xs_ys(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), fibs_2(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys_1(ConsL(z0, z1), z2, z3) -> ConsL(plus#2(z2, z0), zipwith_l#3(z3, z1)) fibs_2#1(zipwith_l, plus, tail_l, z0) -> ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))) zipwith_l#3(z0, z1) -> zipwith_l_f_xs_ys(plus, z0, z1) plus#2(0, z0) -> z0 plus#2(S(z0), z1) -> S(plus#2(z0, z1)) Tuples: PLUS#2(S(z0), z1) -> c5(PLUS#2(z0, z1)) COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) ZIPWITH_L_F_XS_YS#1(plus, fibs, z0, z1) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0)) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3)), S(x4)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x4), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(z0, z1, z2), z3, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3)), S(x4)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, z0)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, z0, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(z0, z1, z2), z3, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, bot[6])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3, x4) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, z0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3, x4) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(z0, z1, z2), z3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3, x4) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x3), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, bot[7])) COND_TAKE_L_N_XS(ConsL(x0, fibs_2(zipwith_l, plus, tail_l)), S(x4)) -> c2(COND_TAKE_L_N_XS(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x4)) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x0, x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, x4) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3)) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, x1)), S(x2)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0])) S tuples: PLUS#2(S(z0), z1) -> c5(PLUS#2(z0, z1)) COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) ZIPWITH_L_F_XS_YS#1(plus, fibs, z0, z1) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0)) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, z0)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, z0, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(z0, z1, z2), z3, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, bot[6])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3, x4) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, z0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3, x4) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(z0, z1, z2), z3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3, x4) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x3), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, bot[7])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x0, x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, x4) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3)) K tuples: COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(z1, z2, z3)), S(z4)) -> c3(COND_TAKE_L_N_XS(zipwith_l_f_xs_ys#1(z1, z2, z3, bot[0]), z4), ZIPWITH_L_F_XS_YS#1(z1, z2, z3, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, fibs_2(z1, z2, z3)), S(z4)) -> c2(COND_TAKE_L_N_XS(fibs_2#1(z1, z2, z3, bot[0]), z4)) Defined Rule Symbols: zipwith_l_f_xs_ys#1_4, cond_zipwith_l_f_xs_ys_2, cond_zipwith_l_f_xs_ys_1_3, fibs_2#1_4, zipwith_l#3_2, plus#2_2 Defined Pair Symbols: PLUS#2_2, COND_ZIPWITH_L_F_XS_YS_1_3, ZIPWITH_L_F_XS_YS#1_4, COND_TAKE_L_N_XS_2, COND_ZIPWITH_L_F_XS_YS_2 Compound Symbols: c5_1, c6_1, c10_1, c3_2, c8_2, c12_2, c2_1, c9_1, c11_1, c3_1 ---------------------------------------- (47) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3)), S(x4)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x4), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(z0, z1, z2), z3, bot[0])) by COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs_2(x1, x2, x3), x4)), S(x5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x1, x2, x3), x4, bot[0])) ---------------------------------------- (48) Obligation: Complexity Dependency Tuples Problem Rules: zipwith_l_f_xs_ys#1(plus, fibs, z0, z1) -> cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0) zipwith_l_f_xs_ys#1(plus, fibs_2(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3) zipwith_l_f_xs_ys#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), zipwith_l_f_xs_ys(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), fibs_2(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys_1(ConsL(z0, z1), z2, z3) -> ConsL(plus#2(z2, z0), zipwith_l#3(z3, z1)) fibs_2#1(zipwith_l, plus, tail_l, z0) -> ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))) zipwith_l#3(z0, z1) -> zipwith_l_f_xs_ys(plus, z0, z1) plus#2(0, z0) -> z0 plus#2(S(z0), z1) -> S(plus#2(z0, z1)) Tuples: PLUS#2(S(z0), z1) -> c5(PLUS#2(z0, z1)) COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) ZIPWITH_L_F_XS_YS#1(plus, fibs, z0, z1) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0)) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3)), S(x4)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, z0)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, z0, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(z0, z1, z2), z3, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, bot[6])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3, x4) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, z0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3, x4) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(z0, z1, z2), z3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3, x4) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x3), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, bot[7])) COND_TAKE_L_N_XS(ConsL(x0, fibs_2(zipwith_l, plus, tail_l)), S(x4)) -> c2(COND_TAKE_L_N_XS(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x4)) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x0, x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, x4) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3)) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, x1)), S(x2)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs_2(x1, x2, x3), x4)), S(x5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x1, x2, x3), x4, bot[0])) S tuples: PLUS#2(S(z0), z1) -> c5(PLUS#2(z0, z1)) COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) ZIPWITH_L_F_XS_YS#1(plus, fibs, z0, z1) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0)) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, z0)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, z0, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(z0, z1, z2), z3, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, bot[6])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3, x4) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, z0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3, x4) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(z0, z1, z2), z3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3, x4) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x3), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, bot[7])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x0, x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, x4) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3)) K tuples: COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(z1, z2, z3)), S(z4)) -> c3(COND_TAKE_L_N_XS(zipwith_l_f_xs_ys#1(z1, z2, z3, bot[0]), z4), ZIPWITH_L_F_XS_YS#1(z1, z2, z3, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, fibs_2(z1, z2, z3)), S(z4)) -> c2(COND_TAKE_L_N_XS(fibs_2#1(z1, z2, z3, bot[0]), z4)) Defined Rule Symbols: zipwith_l_f_xs_ys#1_4, cond_zipwith_l_f_xs_ys_2, cond_zipwith_l_f_xs_ys_1_3, fibs_2#1_4, zipwith_l#3_2, plus#2_2 Defined Pair Symbols: PLUS#2_2, COND_ZIPWITH_L_F_XS_YS_1_3, ZIPWITH_L_F_XS_YS#1_4, COND_TAKE_L_N_XS_2, COND_ZIPWITH_L_F_XS_YS_2 Compound Symbols: c5_1, c6_1, c10_1, c3_2, c8_2, c12_2, c2_1, c9_1, c11_1, c3_1 ---------------------------------------- (49) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3)), S(x4)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, bot[0])) by COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4)), S(x5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4, bot[0])) ---------------------------------------- (50) Obligation: Complexity Dependency Tuples Problem Rules: zipwith_l_f_xs_ys#1(plus, fibs, z0, z1) -> cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0) zipwith_l_f_xs_ys#1(plus, fibs_2(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3) zipwith_l_f_xs_ys#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), zipwith_l_f_xs_ys(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), fibs_2(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys_1(ConsL(z0, z1), z2, z3) -> ConsL(plus#2(z2, z0), zipwith_l#3(z3, z1)) fibs_2#1(zipwith_l, plus, tail_l, z0) -> ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))) zipwith_l#3(z0, z1) -> zipwith_l_f_xs_ys(plus, z0, z1) plus#2(0, z0) -> z0 plus#2(S(z0), z1) -> S(plus#2(z0, z1)) Tuples: PLUS#2(S(z0), z1) -> c5(PLUS#2(z0, z1)) COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) ZIPWITH_L_F_XS_YS#1(plus, fibs, z0, z1) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0)) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, z0)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, z0, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(z0, z1, z2), z3, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, bot[6])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3, x4) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, z0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3, x4) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(z0, z1, z2), z3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3, x4) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x3), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, bot[7])) COND_TAKE_L_N_XS(ConsL(x0, fibs_2(zipwith_l, plus, tail_l)), S(x4)) -> c2(COND_TAKE_L_N_XS(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x4)) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x0, x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, x4) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3)) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, x1)), S(x2)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs_2(x1, x2, x3), x4)), S(x5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x1, x2, x3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4)), S(x5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4, bot[0])) S tuples: PLUS#2(S(z0), z1) -> c5(PLUS#2(z0, z1)) COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) ZIPWITH_L_F_XS_YS#1(plus, fibs, z0, z1) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0)) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, z0)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, z0, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(z0, z1, z2), z3, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, bot[6])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3, x4) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, z0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3, x4) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(z0, z1, z2), z3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3, x4) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x3), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, bot[7])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x0, x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, x4) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3)) K tuples: COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(z1, z2, z3)), S(z4)) -> c3(COND_TAKE_L_N_XS(zipwith_l_f_xs_ys#1(z1, z2, z3, bot[0]), z4), ZIPWITH_L_F_XS_YS#1(z1, z2, z3, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, fibs_2(z1, z2, z3)), S(z4)) -> c2(COND_TAKE_L_N_XS(fibs_2#1(z1, z2, z3, bot[0]), z4)) Defined Rule Symbols: zipwith_l_f_xs_ys#1_4, cond_zipwith_l_f_xs_ys_2, cond_zipwith_l_f_xs_ys_1_3, fibs_2#1_4, zipwith_l#3_2, plus#2_2 Defined Pair Symbols: PLUS#2_2, COND_ZIPWITH_L_F_XS_YS_1_3, ZIPWITH_L_F_XS_YS#1_4, COND_ZIPWITH_L_F_XS_YS_2, COND_TAKE_L_N_XS_2 Compound Symbols: c5_1, c6_1, c10_1, c8_2, c12_2, c2_1, c9_1, c11_1, c3_2, c3_1 ---------------------------------------- (51) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, z0)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, z0, bot[6])) by COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, x2)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6])) ---------------------------------------- (52) Obligation: Complexity Dependency Tuples Problem Rules: zipwith_l_f_xs_ys#1(plus, fibs, z0, z1) -> cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0) zipwith_l_f_xs_ys#1(plus, fibs_2(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3) zipwith_l_f_xs_ys#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), zipwith_l_f_xs_ys(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), fibs_2(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys_1(ConsL(z0, z1), z2, z3) -> ConsL(plus#2(z2, z0), zipwith_l#3(z3, z1)) fibs_2#1(zipwith_l, plus, tail_l, z0) -> ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))) zipwith_l#3(z0, z1) -> zipwith_l_f_xs_ys(plus, z0, z1) plus#2(0, z0) -> z0 plus#2(S(z0), z1) -> S(plus#2(z0, z1)) Tuples: PLUS#2(S(z0), z1) -> c5(PLUS#2(z0, z1)) COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) ZIPWITH_L_F_XS_YS#1(plus, fibs, z0, z1) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0)) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(z0, z1, z2), z3, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, bot[6])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3, x4) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, z0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3, x4) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(z0, z1, z2), z3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3, x4) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x3), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, bot[7])) COND_TAKE_L_N_XS(ConsL(x0, fibs_2(zipwith_l, plus, tail_l)), S(x4)) -> c2(COND_TAKE_L_N_XS(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x4)) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x0, x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, x4) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3)) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, x1)), S(x2)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs_2(x1, x2, x3), x4)), S(x5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x1, x2, x3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4)), S(x5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, x2)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6])) S tuples: PLUS#2(S(z0), z1) -> c5(PLUS#2(z0, z1)) COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) ZIPWITH_L_F_XS_YS#1(plus, fibs, z0, z1) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0)) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(z0, z1, z2), z3, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, bot[6])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3, x4) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, z0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3, x4) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(z0, z1, z2), z3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3, x4) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x3), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, bot[7])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x0, x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, x4) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3)) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, x2)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6])) K tuples: COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(z1, z2, z3)), S(z4)) -> c3(COND_TAKE_L_N_XS(zipwith_l_f_xs_ys#1(z1, z2, z3, bot[0]), z4), ZIPWITH_L_F_XS_YS#1(z1, z2, z3, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, fibs_2(z1, z2, z3)), S(z4)) -> c2(COND_TAKE_L_N_XS(fibs_2#1(z1, z2, z3, bot[0]), z4)) Defined Rule Symbols: zipwith_l_f_xs_ys#1_4, cond_zipwith_l_f_xs_ys_2, cond_zipwith_l_f_xs_ys_1_3, fibs_2#1_4, zipwith_l#3_2, plus#2_2 Defined Pair Symbols: PLUS#2_2, COND_ZIPWITH_L_F_XS_YS_1_3, ZIPWITH_L_F_XS_YS#1_4, COND_ZIPWITH_L_F_XS_YS_2, COND_TAKE_L_N_XS_2 Compound Symbols: c5_1, c6_1, c10_1, c8_2, c12_2, c2_1, c9_1, c11_1, c3_2, c3_1, c8_1 ---------------------------------------- (53) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(z0, z1, z2), z3, bot[6])) by COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[6])) ---------------------------------------- (54) Obligation: Complexity Dependency Tuples Problem Rules: zipwith_l_f_xs_ys#1(plus, fibs, z0, z1) -> cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0) zipwith_l_f_xs_ys#1(plus, fibs_2(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3) zipwith_l_f_xs_ys#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), zipwith_l_f_xs_ys(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), fibs_2(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys_1(ConsL(z0, z1), z2, z3) -> ConsL(plus#2(z2, z0), zipwith_l#3(z3, z1)) fibs_2#1(zipwith_l, plus, tail_l, z0) -> ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))) zipwith_l#3(z0, z1) -> zipwith_l_f_xs_ys(plus, z0, z1) plus#2(0, z0) -> z0 plus#2(S(z0), z1) -> S(plus#2(z0, z1)) Tuples: PLUS#2(S(z0), z1) -> c5(PLUS#2(z0, z1)) COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) ZIPWITH_L_F_XS_YS#1(plus, fibs, z0, z1) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0)) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, bot[6])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3, x4) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, z0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3, x4) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(z0, z1, z2), z3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3, x4) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x3), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, bot[7])) COND_TAKE_L_N_XS(ConsL(x0, fibs_2(zipwith_l, plus, tail_l)), S(x4)) -> c2(COND_TAKE_L_N_XS(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x4)) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x0, x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, x4) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3)) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, x1)), S(x2)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs_2(x1, x2, x3), x4)), S(x5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x1, x2, x3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4)), S(x5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, x2)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[6])) S tuples: PLUS#2(S(z0), z1) -> c5(PLUS#2(z0, z1)) COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) ZIPWITH_L_F_XS_YS#1(plus, fibs, z0, z1) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0)) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, bot[6])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3, x4) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, z0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3, x4) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(z0, z1, z2), z3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3, x4) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x3), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, bot[7])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x0, x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, x4) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3)) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, x2)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[6])) K tuples: COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(z1, z2, z3)), S(z4)) -> c3(COND_TAKE_L_N_XS(zipwith_l_f_xs_ys#1(z1, z2, z3, bot[0]), z4), ZIPWITH_L_F_XS_YS#1(z1, z2, z3, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, fibs_2(z1, z2, z3)), S(z4)) -> c2(COND_TAKE_L_N_XS(fibs_2#1(z1, z2, z3, bot[0]), z4)) Defined Rule Symbols: zipwith_l_f_xs_ys#1_4, cond_zipwith_l_f_xs_ys_2, cond_zipwith_l_f_xs_ys_1_3, fibs_2#1_4, zipwith_l#3_2, plus#2_2 Defined Pair Symbols: PLUS#2_2, COND_ZIPWITH_L_F_XS_YS_1_3, ZIPWITH_L_F_XS_YS#1_4, COND_ZIPWITH_L_F_XS_YS_2, COND_TAKE_L_N_XS_2 Compound Symbols: c5_1, c6_1, c10_1, c8_2, c12_2, c2_1, c9_1, c11_1, c3_2, c3_1, c8_1 ---------------------------------------- (55) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, bot[6])) by COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[6])) ---------------------------------------- (56) Obligation: Complexity Dependency Tuples Problem Rules: zipwith_l_f_xs_ys#1(plus, fibs, z0, z1) -> cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0) zipwith_l_f_xs_ys#1(plus, fibs_2(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3) zipwith_l_f_xs_ys#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), zipwith_l_f_xs_ys(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), fibs_2(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys_1(ConsL(z0, z1), z2, z3) -> ConsL(plus#2(z2, z0), zipwith_l#3(z3, z1)) fibs_2#1(zipwith_l, plus, tail_l, z0) -> ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))) zipwith_l#3(z0, z1) -> zipwith_l_f_xs_ys(plus, z0, z1) plus#2(0, z0) -> z0 plus#2(S(z0), z1) -> S(plus#2(z0, z1)) Tuples: PLUS#2(S(z0), z1) -> c5(PLUS#2(z0, z1)) COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) ZIPWITH_L_F_XS_YS#1(plus, fibs, z0, z1) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3, x4) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, z0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3, x4) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(z0, z1, z2), z3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3, x4) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x3), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, bot[7])) COND_TAKE_L_N_XS(ConsL(x0, fibs_2(zipwith_l, plus, tail_l)), S(x4)) -> c2(COND_TAKE_L_N_XS(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x4)) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x0, x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, x4) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3)) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, x1)), S(x2)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs_2(x1, x2, x3), x4)), S(x5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x1, x2, x3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4)), S(x5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, x2)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[6])) S tuples: PLUS#2(S(z0), z1) -> c5(PLUS#2(z0, z1)) COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) ZIPWITH_L_F_XS_YS#1(plus, fibs, z0, z1) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3, x4) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, z0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3, x4) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(z0, z1, z2), z3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3, x4) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x3), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, bot[7])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x0, x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, x4) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3)) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, x2)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[6])) K tuples: COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(z1, z2, z3)), S(z4)) -> c3(COND_TAKE_L_N_XS(zipwith_l_f_xs_ys#1(z1, z2, z3, bot[0]), z4), ZIPWITH_L_F_XS_YS#1(z1, z2, z3, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, fibs_2(z1, z2, z3)), S(z4)) -> c2(COND_TAKE_L_N_XS(fibs_2#1(z1, z2, z3, bot[0]), z4)) Defined Rule Symbols: zipwith_l_f_xs_ys#1_4, cond_zipwith_l_f_xs_ys_2, cond_zipwith_l_f_xs_ys_1_3, fibs_2#1_4, zipwith_l#3_2, plus#2_2 Defined Pair Symbols: PLUS#2_2, COND_ZIPWITH_L_F_XS_YS_1_3, ZIPWITH_L_F_XS_YS#1_4, COND_TAKE_L_N_XS_2, COND_ZIPWITH_L_F_XS_YS_2 Compound Symbols: c5_1, c6_1, c10_1, c12_2, c2_1, c9_1, c11_1, c3_2, c3_1, c8_2, c8_1 ---------------------------------------- (57) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3, x4) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, z0, bot[7])) by ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4)), x1, x2) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4)), x1, x2) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x0), x1, x2) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7])) ---------------------------------------- (58) Obligation: Complexity Dependency Tuples Problem Rules: zipwith_l_f_xs_ys#1(plus, fibs, z0, z1) -> cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0) zipwith_l_f_xs_ys#1(plus, fibs_2(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3) zipwith_l_f_xs_ys#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), zipwith_l_f_xs_ys(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), fibs_2(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys_1(ConsL(z0, z1), z2, z3) -> ConsL(plus#2(z2, z0), zipwith_l#3(z3, z1)) fibs_2#1(zipwith_l, plus, tail_l, z0) -> ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))) zipwith_l#3(z0, z1) -> zipwith_l_f_xs_ys(plus, z0, z1) plus#2(0, z0) -> z0 plus#2(S(z0), z1) -> S(plus#2(z0, z1)) Tuples: PLUS#2(S(z0), z1) -> c5(PLUS#2(z0, z1)) COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) ZIPWITH_L_F_XS_YS#1(plus, fibs, z0, z1) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3, x4) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(z0, z1, z2), z3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3, x4) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x3), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, bot[7])) COND_TAKE_L_N_XS(ConsL(x0, fibs_2(zipwith_l, plus, tail_l)), S(x4)) -> c2(COND_TAKE_L_N_XS(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x4)) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x0, x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, x4) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3)) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, x1)), S(x2)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs_2(x1, x2, x3), x4)), S(x5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x1, x2, x3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4)), S(x5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, x2)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[6])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4)), x1, x2) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4)), x1, x2) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x0), x1, x2) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7])) S tuples: PLUS#2(S(z0), z1) -> c5(PLUS#2(z0, z1)) COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) ZIPWITH_L_F_XS_YS#1(plus, fibs, z0, z1) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3, x4) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(z0, z1, z2), z3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3, x4) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x3), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, bot[7])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x0, x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, x4) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3)) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, x2)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[6])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4)), x1, x2) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4)), x1, x2) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x0), x1, x2) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7])) K tuples: COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(z1, z2, z3)), S(z4)) -> c3(COND_TAKE_L_N_XS(zipwith_l_f_xs_ys#1(z1, z2, z3, bot[0]), z4), ZIPWITH_L_F_XS_YS#1(z1, z2, z3, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, fibs_2(z1, z2, z3)), S(z4)) -> c2(COND_TAKE_L_N_XS(fibs_2#1(z1, z2, z3, bot[0]), z4)) Defined Rule Symbols: zipwith_l_f_xs_ys#1_4, cond_zipwith_l_f_xs_ys_2, cond_zipwith_l_f_xs_ys_1_3, fibs_2#1_4, zipwith_l#3_2, plus#2_2 Defined Pair Symbols: PLUS#2_2, COND_ZIPWITH_L_F_XS_YS_1_3, ZIPWITH_L_F_XS_YS#1_4, COND_TAKE_L_N_XS_2, COND_ZIPWITH_L_F_XS_YS_2 Compound Symbols: c5_1, c6_1, c10_1, c12_2, c2_1, c9_1, c11_1, c3_2, c3_1, c8_2, c8_1, c12_1 ---------------------------------------- (59) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3, x4) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(z0, z1, z2), z3, bot[7])) by ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x0, x1, x2), x3), x4, x5) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x0, x1, x2), x3, bot[7])) ---------------------------------------- (60) Obligation: Complexity Dependency Tuples Problem Rules: zipwith_l_f_xs_ys#1(plus, fibs, z0, z1) -> cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0) zipwith_l_f_xs_ys#1(plus, fibs_2(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3) zipwith_l_f_xs_ys#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), zipwith_l_f_xs_ys(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), fibs_2(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys_1(ConsL(z0, z1), z2, z3) -> ConsL(plus#2(z2, z0), zipwith_l#3(z3, z1)) fibs_2#1(zipwith_l, plus, tail_l, z0) -> ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))) zipwith_l#3(z0, z1) -> zipwith_l_f_xs_ys(plus, z0, z1) plus#2(0, z0) -> z0 plus#2(S(z0), z1) -> S(plus#2(z0, z1)) Tuples: PLUS#2(S(z0), z1) -> c5(PLUS#2(z0, z1)) COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) ZIPWITH_L_F_XS_YS#1(plus, fibs, z0, z1) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3, x4) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x3), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, bot[7])) COND_TAKE_L_N_XS(ConsL(x0, fibs_2(zipwith_l, plus, tail_l)), S(x4)) -> c2(COND_TAKE_L_N_XS(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x4)) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x0, x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, x4) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3)) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, x1)), S(x2)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs_2(x1, x2, x3), x4)), S(x5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x1, x2, x3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4)), S(x5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, x2)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[6])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4)), x1, x2) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4)), x1, x2) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x0), x1, x2) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x0, x1, x2), x3), x4, x5) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x0, x1, x2), x3, bot[7])) S tuples: PLUS#2(S(z0), z1) -> c5(PLUS#2(z0, z1)) COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) ZIPWITH_L_F_XS_YS#1(plus, fibs, z0, z1) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3, x4) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x3), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, bot[7])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x0, x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, x4) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3)) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, x2)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[6])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4)), x1, x2) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4)), x1, x2) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x0), x1, x2) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x0, x1, x2), x3), x4, x5) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x0, x1, x2), x3, bot[7])) K tuples: COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(z1, z2, z3)), S(z4)) -> c3(COND_TAKE_L_N_XS(zipwith_l_f_xs_ys#1(z1, z2, z3, bot[0]), z4), ZIPWITH_L_F_XS_YS#1(z1, z2, z3, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, fibs_2(z1, z2, z3)), S(z4)) -> c2(COND_TAKE_L_N_XS(fibs_2#1(z1, z2, z3, bot[0]), z4)) Defined Rule Symbols: zipwith_l_f_xs_ys#1_4, cond_zipwith_l_f_xs_ys_2, cond_zipwith_l_f_xs_ys_1_3, fibs_2#1_4, zipwith_l#3_2, plus#2_2 Defined Pair Symbols: PLUS#2_2, COND_ZIPWITH_L_F_XS_YS_1_3, ZIPWITH_L_F_XS_YS#1_4, COND_TAKE_L_N_XS_2, COND_ZIPWITH_L_F_XS_YS_2 Compound Symbols: c5_1, c6_1, c10_1, c12_2, c2_1, c9_1, c11_1, c3_2, c3_1, c8_2, c8_1, c12_1 ---------------------------------------- (61) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3, x4) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x3), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, bot[7])) by ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3), x4, x5) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3, bot[7])) ---------------------------------------- (62) Obligation: Complexity Dependency Tuples Problem Rules: zipwith_l_f_xs_ys#1(plus, fibs, z0, z1) -> cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0) zipwith_l_f_xs_ys#1(plus, fibs_2(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3) zipwith_l_f_xs_ys#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), zipwith_l_f_xs_ys(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), fibs_2(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys_1(ConsL(z0, z1), z2, z3) -> ConsL(plus#2(z2, z0), zipwith_l#3(z3, z1)) fibs_2#1(zipwith_l, plus, tail_l, z0) -> ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))) zipwith_l#3(z0, z1) -> zipwith_l_f_xs_ys(plus, z0, z1) plus#2(0, z0) -> z0 plus#2(S(z0), z1) -> S(plus#2(z0, z1)) Tuples: PLUS#2(S(z0), z1) -> c5(PLUS#2(z0, z1)) COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) ZIPWITH_L_F_XS_YS#1(plus, fibs, z0, z1) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0)) COND_TAKE_L_N_XS(ConsL(x0, fibs_2(zipwith_l, plus, tail_l)), S(x4)) -> c2(COND_TAKE_L_N_XS(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x4)) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x0, x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, x4) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3)) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, x1)), S(x2)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs_2(x1, x2, x3), x4)), S(x5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x1, x2, x3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4)), S(x5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, x2)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[6])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4)), x1, x2) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4)), x1, x2) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x0), x1, x2) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x0, x1, x2), x3), x4, x5) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x0, x1, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3), x4, x5) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3, bot[7])) S tuples: PLUS#2(S(z0), z1) -> c5(PLUS#2(z0, z1)) COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) ZIPWITH_L_F_XS_YS#1(plus, fibs, z0, z1) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0)) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x0, x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, x4) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3)) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, x2)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[6])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4)), x1, x2) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4)), x1, x2) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x0), x1, x2) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x0, x1, x2), x3), x4, x5) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x0, x1, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3), x4, x5) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3, bot[7])) K tuples: COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(z1, z2, z3)), S(z4)) -> c3(COND_TAKE_L_N_XS(zipwith_l_f_xs_ys#1(z1, z2, z3, bot[0]), z4), ZIPWITH_L_F_XS_YS#1(z1, z2, z3, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, fibs_2(z1, z2, z3)), S(z4)) -> c2(COND_TAKE_L_N_XS(fibs_2#1(z1, z2, z3, bot[0]), z4)) Defined Rule Symbols: zipwith_l_f_xs_ys#1_4, cond_zipwith_l_f_xs_ys_2, cond_zipwith_l_f_xs_ys_1_3, fibs_2#1_4, zipwith_l#3_2, plus#2_2 Defined Pair Symbols: PLUS#2_2, COND_ZIPWITH_L_F_XS_YS_1_3, ZIPWITH_L_F_XS_YS#1_4, COND_TAKE_L_N_XS_2, COND_ZIPWITH_L_F_XS_YS_2 Compound Symbols: c5_1, c6_1, c10_1, c2_1, c9_1, c11_1, c3_2, c3_1, c8_2, c8_1, c12_2, c12_1 ---------------------------------------- (63) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace COND_TAKE_L_N_XS(ConsL(x0, fibs_2(zipwith_l, plus, tail_l)), S(x4)) -> c2(COND_TAKE_L_N_XS(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x4)) by COND_TAKE_L_N_XS(ConsL(x0, fibs_2(zipwith_l, plus, tail_l)), S(x1)) -> c2(COND_TAKE_L_N_XS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x1)) ---------------------------------------- (64) Obligation: Complexity Dependency Tuples Problem Rules: zipwith_l_f_xs_ys#1(plus, fibs, z0, z1) -> cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0) zipwith_l_f_xs_ys#1(plus, fibs_2(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3) zipwith_l_f_xs_ys#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), zipwith_l_f_xs_ys(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), fibs_2(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys_1(ConsL(z0, z1), z2, z3) -> ConsL(plus#2(z2, z0), zipwith_l#3(z3, z1)) fibs_2#1(zipwith_l, plus, tail_l, z0) -> ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))) zipwith_l#3(z0, z1) -> zipwith_l_f_xs_ys(plus, z0, z1) plus#2(0, z0) -> z0 plus#2(S(z0), z1) -> S(plus#2(z0, z1)) Tuples: PLUS#2(S(z0), z1) -> c5(PLUS#2(z0, z1)) COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) ZIPWITH_L_F_XS_YS#1(plus, fibs, z0, z1) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0)) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x0, x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, x4) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3)) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, x1)), S(x2)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs_2(x1, x2, x3), x4)), S(x5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x1, x2, x3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4)), S(x5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, x2)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[6])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4)), x1, x2) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4)), x1, x2) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x0), x1, x2) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x0, x1, x2), x3), x4, x5) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x0, x1, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3), x4, x5) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3, bot[7])) COND_TAKE_L_N_XS(ConsL(x0, fibs_2(zipwith_l, plus, tail_l)), S(x1)) -> c2(COND_TAKE_L_N_XS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x1)) S tuples: PLUS#2(S(z0), z1) -> c5(PLUS#2(z0, z1)) COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) ZIPWITH_L_F_XS_YS#1(plus, fibs, z0, z1) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0)) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x0, x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, x4) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3)) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, x2)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[6])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4)), x1, x2) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4)), x1, x2) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x0), x1, x2) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x0, x1, x2), x3), x4, x5) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x0, x1, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3), x4, x5) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3, bot[7])) K tuples: COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(z1, z2, z3)), S(z4)) -> c3(COND_TAKE_L_N_XS(zipwith_l_f_xs_ys#1(z1, z2, z3, bot[0]), z4), ZIPWITH_L_F_XS_YS#1(z1, z2, z3, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, fibs_2(z1, z2, z3)), S(z4)) -> c2(COND_TAKE_L_N_XS(fibs_2#1(z1, z2, z3, bot[0]), z4)) Defined Rule Symbols: zipwith_l_f_xs_ys#1_4, cond_zipwith_l_f_xs_ys_2, cond_zipwith_l_f_xs_ys_1_3, fibs_2#1_4, zipwith_l#3_2, plus#2_2 Defined Pair Symbols: PLUS#2_2, COND_ZIPWITH_L_F_XS_YS_1_3, ZIPWITH_L_F_XS_YS#1_4, COND_ZIPWITH_L_F_XS_YS_2, COND_TAKE_L_N_XS_2 Compound Symbols: c5_1, c6_1, c10_1, c9_1, c11_1, c3_2, c3_1, c8_2, c8_1, c12_2, c12_1, c2_1 ---------------------------------------- (65) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x0, x1)) by COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0, x1)) ---------------------------------------- (66) Obligation: Complexity Dependency Tuples Problem Rules: zipwith_l_f_xs_ys#1(plus, fibs, z0, z1) -> cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0) zipwith_l_f_xs_ys#1(plus, fibs_2(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3) zipwith_l_f_xs_ys#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), zipwith_l_f_xs_ys(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), fibs_2(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys_1(ConsL(z0, z1), z2, z3) -> ConsL(plus#2(z2, z0), zipwith_l#3(z3, z1)) fibs_2#1(zipwith_l, plus, tail_l, z0) -> ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))) zipwith_l#3(z0, z1) -> zipwith_l_f_xs_ys(plus, z0, z1) plus#2(0, z0) -> z0 plus#2(S(z0), z1) -> S(plus#2(z0, z1)) Tuples: PLUS#2(S(z0), z1) -> c5(PLUS#2(z0, z1)) COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) ZIPWITH_L_F_XS_YS#1(plus, fibs, z0, z1) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, x4) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3)) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, x1)), S(x2)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs_2(x1, x2, x3), x4)), S(x5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x1, x2, x3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4)), S(x5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, x2)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[6])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4)), x1, x2) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4)), x1, x2) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x0), x1, x2) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x0, x1, x2), x3), x4, x5) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x0, x1, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3), x4, x5) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3, bot[7])) COND_TAKE_L_N_XS(ConsL(x0, fibs_2(zipwith_l, plus, tail_l)), S(x1)) -> c2(COND_TAKE_L_N_XS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x1)) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0, x1)) S tuples: PLUS#2(S(z0), z1) -> c5(PLUS#2(z0, z1)) COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) ZIPWITH_L_F_XS_YS#1(plus, fibs, z0, z1) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, x4) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3)) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, x2)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[6])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4)), x1, x2) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4)), x1, x2) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x0), x1, x2) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x0, x1, x2), x3), x4, x5) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x0, x1, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3), x4, x5) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3, bot[7])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0, x1)) K tuples: COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(z1, z2, z3)), S(z4)) -> c3(COND_TAKE_L_N_XS(zipwith_l_f_xs_ys#1(z1, z2, z3, bot[0]), z4), ZIPWITH_L_F_XS_YS#1(z1, z2, z3, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, fibs_2(z1, z2, z3)), S(z4)) -> c2(COND_TAKE_L_N_XS(fibs_2#1(z1, z2, z3, bot[0]), z4)) Defined Rule Symbols: zipwith_l_f_xs_ys#1_4, cond_zipwith_l_f_xs_ys_2, cond_zipwith_l_f_xs_ys_1_3, fibs_2#1_4, zipwith_l#3_2, plus#2_2 Defined Pair Symbols: PLUS#2_2, COND_ZIPWITH_L_F_XS_YS_1_3, ZIPWITH_L_F_XS_YS#1_4, COND_TAKE_L_N_XS_2, COND_ZIPWITH_L_F_XS_YS_2 Compound Symbols: c5_1, c6_1, c10_1, c11_1, c3_2, c3_1, c8_2, c8_1, c12_2, c12_1, c2_1, c9_1 ---------------------------------------- (67) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, x4) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3)) by ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x0, x1) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0)) ---------------------------------------- (68) Obligation: Complexity Dependency Tuples Problem Rules: zipwith_l_f_xs_ys#1(plus, fibs, z0, z1) -> cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0) zipwith_l_f_xs_ys#1(plus, fibs_2(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3) zipwith_l_f_xs_ys#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), zipwith_l_f_xs_ys(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), fibs_2(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys_1(ConsL(z0, z1), z2, z3) -> ConsL(plus#2(z2, z0), zipwith_l#3(z3, z1)) fibs_2#1(zipwith_l, plus, tail_l, z0) -> ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))) zipwith_l#3(z0, z1) -> zipwith_l_f_xs_ys(plus, z0, z1) plus#2(0, z0) -> z0 plus#2(S(z0), z1) -> S(plus#2(z0, z1)) Tuples: PLUS#2(S(z0), z1) -> c5(PLUS#2(z0, z1)) COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) ZIPWITH_L_F_XS_YS#1(plus, fibs, z0, z1) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0)) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, x1)), S(x2)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs_2(x1, x2, x3), x4)), S(x5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x1, x2, x3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4)), S(x5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, x2)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[6])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4)), x1, x2) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4)), x1, x2) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x0), x1, x2) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x0, x1, x2), x3), x4, x5) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x0, x1, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3), x4, x5) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3, bot[7])) COND_TAKE_L_N_XS(ConsL(x0, fibs_2(zipwith_l, plus, tail_l)), S(x1)) -> c2(COND_TAKE_L_N_XS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x1)) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0, x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x0, x1) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0)) S tuples: PLUS#2(S(z0), z1) -> c5(PLUS#2(z0, z1)) COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) ZIPWITH_L_F_XS_YS#1(plus, fibs, z0, z1) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0)) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, x2)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[6])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4)), x1, x2) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4)), x1, x2) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x0), x1, x2) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x0, x1, x2), x3), x4, x5) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x0, x1, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3), x4, x5) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3, bot[7])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0, x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x0, x1) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0)) K tuples: COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(z1, z2, z3)), S(z4)) -> c3(COND_TAKE_L_N_XS(zipwith_l_f_xs_ys#1(z1, z2, z3, bot[0]), z4), ZIPWITH_L_F_XS_YS#1(z1, z2, z3, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, fibs_2(z1, z2, z3)), S(z4)) -> c2(COND_TAKE_L_N_XS(fibs_2#1(z1, z2, z3, bot[0]), z4)) Defined Rule Symbols: zipwith_l_f_xs_ys#1_4, cond_zipwith_l_f_xs_ys_2, cond_zipwith_l_f_xs_ys_1_3, fibs_2#1_4, zipwith_l#3_2, plus#2_2 Defined Pair Symbols: PLUS#2_2, COND_ZIPWITH_L_F_XS_YS_1_3, ZIPWITH_L_F_XS_YS#1_4, COND_TAKE_L_N_XS_2, COND_ZIPWITH_L_F_XS_YS_2 Compound Symbols: c5_1, c6_1, c10_1, c3_2, c3_1, c8_2, c8_1, c12_2, c12_1, c2_1, c9_1, c11_1 ---------------------------------------- (69) CdtRewritingProof (BOTH BOUNDS(ID, ID)) Used rewriting to replace COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[0])) by COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z1)), S(z2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z1), z2), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z1, bot[0])) ---------------------------------------- (70) Obligation: Complexity Dependency Tuples Problem Rules: zipwith_l_f_xs_ys#1(plus, fibs, z0, z1) -> cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0) zipwith_l_f_xs_ys#1(plus, fibs_2(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3) zipwith_l_f_xs_ys#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), zipwith_l_f_xs_ys(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), fibs_2(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys_1(ConsL(z0, z1), z2, z3) -> ConsL(plus#2(z2, z0), zipwith_l#3(z3, z1)) fibs_2#1(zipwith_l, plus, tail_l, z0) -> ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))) zipwith_l#3(z0, z1) -> zipwith_l_f_xs_ys(plus, z0, z1) plus#2(0, z0) -> z0 plus#2(S(z0), z1) -> S(plus#2(z0, z1)) Tuples: PLUS#2(S(z0), z1) -> c5(PLUS#2(z0, z1)) COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) ZIPWITH_L_F_XS_YS#1(plus, fibs, z0, z1) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0)) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, x1)), S(x2)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs_2(x1, x2, x3), x4)), S(x5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x1, x2, x3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4)), S(x5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, x2)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[6])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4)), x1, x2) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4)), x1, x2) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x0), x1, x2) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x0, x1, x2), x3), x4, x5) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x0, x1, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3), x4, x5) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3, bot[7])) COND_TAKE_L_N_XS(ConsL(x0, fibs_2(zipwith_l, plus, tail_l)), S(x1)) -> c2(COND_TAKE_L_N_XS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x1)) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0, x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x0, x1) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0)) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z1)), S(z2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z1), z2), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z1, bot[0])) S tuples: PLUS#2(S(z0), z1) -> c5(PLUS#2(z0, z1)) COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) ZIPWITH_L_F_XS_YS#1(plus, fibs, z0, z1) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0)) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, x2)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[6])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4)), x1, x2) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4)), x1, x2) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x0), x1, x2) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x0, x1, x2), x3), x4, x5) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x0, x1, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3), x4, x5) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3, bot[7])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0, x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x0, x1) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0)) K tuples: COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(z1, z2, z3)), S(z4)) -> c3(COND_TAKE_L_N_XS(zipwith_l_f_xs_ys#1(z1, z2, z3, bot[0]), z4), ZIPWITH_L_F_XS_YS#1(z1, z2, z3, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, fibs_2(z1, z2, z3)), S(z4)) -> c2(COND_TAKE_L_N_XS(fibs_2#1(z1, z2, z3, bot[0]), z4)) Defined Rule Symbols: zipwith_l_f_xs_ys#1_4, cond_zipwith_l_f_xs_ys_2, cond_zipwith_l_f_xs_ys_1_3, fibs_2#1_4, zipwith_l#3_2, plus#2_2 Defined Pair Symbols: PLUS#2_2, COND_ZIPWITH_L_F_XS_YS_1_3, ZIPWITH_L_F_XS_YS#1_4, COND_TAKE_L_N_XS_2, COND_ZIPWITH_L_F_XS_YS_2 Compound Symbols: c5_1, c6_1, c10_1, c3_2, c3_1, c8_2, c8_1, c12_2, c12_1, c2_1, c9_1, c11_1 ---------------------------------------- (71) CdtRewritingProof (BOTH BOUNDS(ID, ID)) Used rewriting to replace COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x5, bot[6])) by COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z2)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z2), z0, z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z2, bot[6])) ---------------------------------------- (72) Obligation: Complexity Dependency Tuples Problem Rules: zipwith_l_f_xs_ys#1(plus, fibs, z0, z1) -> cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0) zipwith_l_f_xs_ys#1(plus, fibs_2(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3) zipwith_l_f_xs_ys#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), zipwith_l_f_xs_ys(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), fibs_2(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys_1(ConsL(z0, z1), z2, z3) -> ConsL(plus#2(z2, z0), zipwith_l#3(z3, z1)) fibs_2#1(zipwith_l, plus, tail_l, z0) -> ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))) zipwith_l#3(z0, z1) -> zipwith_l_f_xs_ys(plus, z0, z1) plus#2(0, z0) -> z0 plus#2(S(z0), z1) -> S(plus#2(z0, z1)) Tuples: PLUS#2(S(z0), z1) -> c5(PLUS#2(z0, z1)) COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) ZIPWITH_L_F_XS_YS#1(plus, fibs, z0, z1) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0)) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, x1)), S(x2)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs_2(x1, x2, x3), x4)), S(x5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x1, x2, x3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4)), S(x5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, x2)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[6])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4)), x1, x2) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4)), x1, x2) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x0), x1, x2) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x0, x1, x2), x3), x4, x5) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x0, x1, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3), x4, x5) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3, bot[7])) COND_TAKE_L_N_XS(ConsL(x0, fibs_2(zipwith_l, plus, tail_l)), S(x1)) -> c2(COND_TAKE_L_N_XS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x1)) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0, x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x0, x1) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0)) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z1)), S(z2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z1), z2), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z1, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z2)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z2), z0, z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z2, bot[6])) S tuples: PLUS#2(S(z0), z1) -> c5(PLUS#2(z0, z1)) COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) ZIPWITH_L_F_XS_YS#1(plus, fibs, z0, z1) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0)) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, x2)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[6])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4)), x1, x2) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4)), x1, x2) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x0), x1, x2) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x0, x1, x2), x3), x4, x5) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x0, x1, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3), x4, x5) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3, bot[7])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0, x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x0, x1) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0)) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z2)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z2), z0, z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z2, bot[6])) K tuples: COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(z1, z2, z3)), S(z4)) -> c3(COND_TAKE_L_N_XS(zipwith_l_f_xs_ys#1(z1, z2, z3, bot[0]), z4), ZIPWITH_L_F_XS_YS#1(z1, z2, z3, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, fibs_2(z1, z2, z3)), S(z4)) -> c2(COND_TAKE_L_N_XS(fibs_2#1(z1, z2, z3, bot[0]), z4)) Defined Rule Symbols: zipwith_l_f_xs_ys#1_4, cond_zipwith_l_f_xs_ys_2, cond_zipwith_l_f_xs_ys_1_3, fibs_2#1_4, zipwith_l#3_2, plus#2_2 Defined Pair Symbols: PLUS#2_2, COND_ZIPWITH_L_F_XS_YS_1_3, ZIPWITH_L_F_XS_YS#1_4, COND_TAKE_L_N_XS_2, COND_ZIPWITH_L_F_XS_YS_2 Compound Symbols: c5_1, c6_1, c10_1, c3_2, c3_1, c8_2, c8_1, c12_2, c12_1, c2_1, c9_1, c11_1 ---------------------------------------- (73) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace PLUS#2(S(z0), z1) -> c5(PLUS#2(z0, z1)) by PLUS#2(S(S(y0)), z1) -> c5(PLUS#2(S(y0), z1)) ---------------------------------------- (74) Obligation: Complexity Dependency Tuples Problem Rules: zipwith_l_f_xs_ys#1(plus, fibs, z0, z1) -> cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0) zipwith_l_f_xs_ys#1(plus, fibs_2(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3) zipwith_l_f_xs_ys#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), zipwith_l_f_xs_ys(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), fibs_2(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys_1(ConsL(z0, z1), z2, z3) -> ConsL(plus#2(z2, z0), zipwith_l#3(z3, z1)) fibs_2#1(zipwith_l, plus, tail_l, z0) -> ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))) zipwith_l#3(z0, z1) -> zipwith_l_f_xs_ys(plus, z0, z1) plus#2(0, z0) -> z0 plus#2(S(z0), z1) -> S(plus#2(z0, z1)) Tuples: COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) ZIPWITH_L_F_XS_YS#1(plus, fibs, z0, z1) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0)) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, x1)), S(x2)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs_2(x1, x2, x3), x4)), S(x5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x1, x2, x3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4)), S(x5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, x2)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[6])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4)), x1, x2) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4)), x1, x2) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x0), x1, x2) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x0, x1, x2), x3), x4, x5) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x0, x1, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3), x4, x5) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3, bot[7])) COND_TAKE_L_N_XS(ConsL(x0, fibs_2(zipwith_l, plus, tail_l)), S(x1)) -> c2(COND_TAKE_L_N_XS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x1)) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0, x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x0, x1) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0)) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z1)), S(z2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z1), z2), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z1, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z2)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z2), z0, z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z2, bot[6])) PLUS#2(S(S(y0)), z1) -> c5(PLUS#2(S(y0), z1)) S tuples: COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) ZIPWITH_L_F_XS_YS#1(plus, fibs, z0, z1) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0)) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, x2)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[6])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4)), x1, x2) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4)), x1, x2) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x0), x1, x2) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x0, x1, x2), x3), x4, x5) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x0, x1, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3), x4, x5) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3, bot[7])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0, x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x0, x1) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0)) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z2)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z2), z0, z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z2, bot[6])) PLUS#2(S(S(y0)), z1) -> c5(PLUS#2(S(y0), z1)) K tuples: COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(z1, z2, z3)), S(z4)) -> c3(COND_TAKE_L_N_XS(zipwith_l_f_xs_ys#1(z1, z2, z3, bot[0]), z4), ZIPWITH_L_F_XS_YS#1(z1, z2, z3, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, fibs_2(z1, z2, z3)), S(z4)) -> c2(COND_TAKE_L_N_XS(fibs_2#1(z1, z2, z3, bot[0]), z4)) Defined Rule Symbols: zipwith_l_f_xs_ys#1_4, cond_zipwith_l_f_xs_ys_2, cond_zipwith_l_f_xs_ys_1_3, fibs_2#1_4, zipwith_l#3_2, plus#2_2 Defined Pair Symbols: COND_ZIPWITH_L_F_XS_YS_1_3, ZIPWITH_L_F_XS_YS#1_4, COND_TAKE_L_N_XS_2, COND_ZIPWITH_L_F_XS_YS_2, PLUS#2_2 Compound Symbols: c6_1, c10_1, c3_2, c3_1, c8_2, c8_1, c12_2, c12_1, c2_1, c9_1, c11_1, c5_1 ---------------------------------------- (75) CdtInstantiationProof (BOTH BOUNDS(ID, ID)) Use instantiation to replace ZIPWITH_L_F_XS_YS#1(plus, fibs, z0, z1) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0)) by ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x0)) ---------------------------------------- (76) Obligation: Complexity Dependency Tuples Problem Rules: zipwith_l_f_xs_ys#1(plus, fibs, z0, z1) -> cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0) zipwith_l_f_xs_ys#1(plus, fibs_2(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3) zipwith_l_f_xs_ys#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), zipwith_l_f_xs_ys(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), fibs_2(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys_1(ConsL(z0, z1), z2, z3) -> ConsL(plus#2(z2, z0), zipwith_l#3(z3, z1)) fibs_2#1(zipwith_l, plus, tail_l, z0) -> ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))) zipwith_l#3(z0, z1) -> zipwith_l_f_xs_ys(plus, z0, z1) plus#2(0, z0) -> z0 plus#2(S(z0), z1) -> S(plus#2(z0, z1)) Tuples: COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, x1)), S(x2)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs_2(x1, x2, x3), x4)), S(x5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x1, x2, x3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4)), S(x5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, x2)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[6])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4)), x1, x2) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4)), x1, x2) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x0), x1, x2) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x0, x1, x2), x3), x4, x5) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x0, x1, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3), x4, x5) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3, bot[7])) COND_TAKE_L_N_XS(ConsL(x0, fibs_2(zipwith_l, plus, tail_l)), S(x1)) -> c2(COND_TAKE_L_N_XS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x1)) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0, x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x0, x1) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0)) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z1)), S(z2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z1), z2), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z1, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z2)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z2), z0, z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z2, bot[6])) PLUS#2(S(S(y0)), z1) -> c5(PLUS#2(S(y0), z1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x0)) S tuples: COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, x2)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[6])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4)), x1, x2) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4)), x1, x2) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x0), x1, x2) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x0, x1, x2), x3), x4, x5) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x0, x1, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3), x4, x5) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3, bot[7])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0, x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x0, x1) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0)) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z2)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z2), z0, z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z2, bot[6])) PLUS#2(S(S(y0)), z1) -> c5(PLUS#2(S(y0), z1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x0)) K tuples: COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(z1, z2, z3)), S(z4)) -> c3(COND_TAKE_L_N_XS(zipwith_l_f_xs_ys#1(z1, z2, z3, bot[0]), z4), ZIPWITH_L_F_XS_YS#1(z1, z2, z3, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, fibs_2(z1, z2, z3)), S(z4)) -> c2(COND_TAKE_L_N_XS(fibs_2#1(z1, z2, z3, bot[0]), z4)) Defined Rule Symbols: zipwith_l_f_xs_ys#1_4, cond_zipwith_l_f_xs_ys_2, cond_zipwith_l_f_xs_ys_1_3, fibs_2#1_4, zipwith_l#3_2, plus#2_2 Defined Pair Symbols: COND_ZIPWITH_L_F_XS_YS_1_3, COND_TAKE_L_N_XS_2, COND_ZIPWITH_L_F_XS_YS_2, ZIPWITH_L_F_XS_YS#1_4, PLUS#2_2 Compound Symbols: c6_1, c3_2, c3_1, c8_2, c8_1, c12_2, c12_1, c2_1, c9_1, c11_1, c5_1, c10_1 ---------------------------------------- (77) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1))) Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S. ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x1)) We considered the (Usable) Rules:none And the Tuples: COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, x1)), S(x2)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs_2(x1, x2, x3), x4)), S(x5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x1, x2, x3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4)), S(x5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, x2)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[6])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4)), x1, x2) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4)), x1, x2) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x0), x1, x2) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x0, x1, x2), x3), x4, x5) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x0, x1, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3), x4, x5) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3, bot[7])) COND_TAKE_L_N_XS(ConsL(x0, fibs_2(zipwith_l, plus, tail_l)), S(x1)) -> c2(COND_TAKE_L_N_XS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x1)) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0, x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x0, x1) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0)) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z1)), S(z2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z1), z2), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z1, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z2)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z2), z0, z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z2, bot[6])) PLUS#2(S(S(y0)), z1) -> c5(PLUS#2(S(y0), z1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x0)) The order we found is given by the following interpretation: Polynomial interpretation : POL(0) = 0 POL(COND_TAKE_L_N_XS(x_1, x_2)) = x_2 POL(COND_ZIPWITH_L_F_XS_YS(x_1, x_2)) = 0 POL(COND_ZIPWITH_L_F_XS_YS_1(x_1, x_2, x_3)) = 0 POL(ConsL(x_1, x_2)) = 0 POL(PLUS#2(x_1, x_2)) = 0 POL(S(x_1)) = [1] + x_1 POL(ZIPWITH_L_F_XS_YS#1(x_1, x_2, x_3, x_4)) = x_1 + x_4 POL(bot[0]) = [1] POL(bot[6]) = 0 POL(bot[7]) = 0 POL(c10(x_1)) = x_1 POL(c11(x_1)) = x_1 POL(c12(x_1)) = x_1 POL(c12(x_1, x_2)) = x_1 + x_2 POL(c2(x_1)) = x_1 POL(c3(x_1)) = x_1 POL(c3(x_1, x_2)) = x_1 + x_2 POL(c5(x_1)) = x_1 POL(c6(x_1)) = x_1 POL(c8(x_1)) = x_1 POL(c8(x_1, x_2)) = x_1 + x_2 POL(c9(x_1)) = x_1 POL(cond_zipwith_l_f_xs_ys(x_1, x_2)) = 0 POL(cond_zipwith_l_f_xs_ys_1(x_1, x_2, x_3)) = 0 POL(fibs) = 0 POL(fibs_2(x_1, x_2, x_3)) = 0 POL(fibs_2#1(x_1, x_2, x_3, x_4)) = x_1 + x_2 + x_3 POL(plus) = 0 POL(plus#2(x_1, x_2)) = [1] + x_1 + x_2 POL(tail_l) = 0 POL(zipwith_l) = 0 POL(zipwith_l#3(x_1, x_2)) = 0 POL(zipwith_l_f_xs_ys(x_1, x_2, x_3)) = 0 POL(zipwith_l_f_xs_ys#1(x_1, x_2, x_3, x_4)) = x_1 + x_2 + x_3 ---------------------------------------- (78) Obligation: Complexity Dependency Tuples Problem Rules: zipwith_l_f_xs_ys#1(plus, fibs, z0, z1) -> cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0) zipwith_l_f_xs_ys#1(plus, fibs_2(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3) zipwith_l_f_xs_ys#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), zipwith_l_f_xs_ys(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), fibs_2(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys_1(ConsL(z0, z1), z2, z3) -> ConsL(plus#2(z2, z0), zipwith_l#3(z3, z1)) fibs_2#1(zipwith_l, plus, tail_l, z0) -> ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))) zipwith_l#3(z0, z1) -> zipwith_l_f_xs_ys(plus, z0, z1) plus#2(0, z0) -> z0 plus#2(S(z0), z1) -> S(plus#2(z0, z1)) Tuples: COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, x1)), S(x2)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs_2(x1, x2, x3), x4)), S(x5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x1, x2, x3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4)), S(x5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, x2)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[6])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4)), x1, x2) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4)), x1, x2) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x0), x1, x2) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x0, x1, x2), x3), x4, x5) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x0, x1, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3), x4, x5) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3, bot[7])) COND_TAKE_L_N_XS(ConsL(x0, fibs_2(zipwith_l, plus, tail_l)), S(x1)) -> c2(COND_TAKE_L_N_XS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x1)) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0, x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x0, x1) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0)) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z1)), S(z2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z1), z2), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z1, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z2)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z2), z0, z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z2, bot[6])) PLUS#2(S(S(y0)), z1) -> c5(PLUS#2(S(y0), z1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x0)) S tuples: COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, x2)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[6])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4)), x1, x2) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4)), x1, x2) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x0), x1, x2) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x0, x1, x2), x3), x4, x5) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x0, x1, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3), x4, x5) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3, bot[7])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0, x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x0, x1) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0)) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z2)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z2), z0, z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z2, bot[6])) PLUS#2(S(S(y0)), z1) -> c5(PLUS#2(S(y0), z1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x0)) K tuples: COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(z1, z2, z3)), S(z4)) -> c3(COND_TAKE_L_N_XS(zipwith_l_f_xs_ys#1(z1, z2, z3, bot[0]), z4), ZIPWITH_L_F_XS_YS#1(z1, z2, z3, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, fibs_2(z1, z2, z3)), S(z4)) -> c2(COND_TAKE_L_N_XS(fibs_2#1(z1, z2, z3, bot[0]), z4)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x1)) Defined Rule Symbols: zipwith_l_f_xs_ys#1_4, cond_zipwith_l_f_xs_ys_2, cond_zipwith_l_f_xs_ys_1_3, fibs_2#1_4, zipwith_l#3_2, plus#2_2 Defined Pair Symbols: COND_ZIPWITH_L_F_XS_YS_1_3, COND_TAKE_L_N_XS_2, COND_ZIPWITH_L_F_XS_YS_2, ZIPWITH_L_F_XS_YS#1_4, PLUS#2_2 Compound Symbols: c6_1, c3_2, c3_1, c8_2, c8_1, c12_2, c12_1, c2_1, c9_1, c11_1, c5_1, c10_1 ---------------------------------------- (79) CdtInstantiationProof (BOTH BOUNDS(ID, ID)) Use instantiation to replace ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4)), x1, x2) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[7])) by ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ---------------------------------------- (80) Obligation: Complexity Dependency Tuples Problem Rules: zipwith_l_f_xs_ys#1(plus, fibs, z0, z1) -> cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0) zipwith_l_f_xs_ys#1(plus, fibs_2(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3) zipwith_l_f_xs_ys#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), zipwith_l_f_xs_ys(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), fibs_2(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys_1(ConsL(z0, z1), z2, z3) -> ConsL(plus#2(z2, z0), zipwith_l#3(z3, z1)) fibs_2#1(zipwith_l, plus, tail_l, z0) -> ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))) zipwith_l#3(z0, z1) -> zipwith_l_f_xs_ys(plus, z0, z1) plus#2(0, z0) -> z0 plus#2(S(z0), z1) -> S(plus#2(z0, z1)) Tuples: COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, x1)), S(x2)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs_2(x1, x2, x3), x4)), S(x5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x1, x2, x3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4)), S(x5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, x2)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[6])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4)), x1, x2) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x0), x1, x2) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x0, x1, x2), x3), x4, x5) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x0, x1, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3), x4, x5) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3, bot[7])) COND_TAKE_L_N_XS(ConsL(x0, fibs_2(zipwith_l, plus, tail_l)), S(x1)) -> c2(COND_TAKE_L_N_XS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x1)) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0, x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x0, x1) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0)) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z1)), S(z2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z1), z2), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z1, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z2)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z2), z0, z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z2, bot[6])) PLUS#2(S(S(y0)), z1) -> c5(PLUS#2(S(y0), z1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x0)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) S tuples: COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, x2)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[6])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4)), x1, x2) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x0), x1, x2) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x0, x1, x2), x3), x4, x5) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x0, x1, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3), x4, x5) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3, bot[7])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0, x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x0, x1) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0)) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z2)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z2), z0, z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z2, bot[6])) PLUS#2(S(S(y0)), z1) -> c5(PLUS#2(S(y0), z1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x0)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) K tuples: COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(z1, z2, z3)), S(z4)) -> c3(COND_TAKE_L_N_XS(zipwith_l_f_xs_ys#1(z1, z2, z3, bot[0]), z4), ZIPWITH_L_F_XS_YS#1(z1, z2, z3, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, fibs_2(z1, z2, z3)), S(z4)) -> c2(COND_TAKE_L_N_XS(fibs_2#1(z1, z2, z3, bot[0]), z4)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x1)) Defined Rule Symbols: zipwith_l_f_xs_ys#1_4, cond_zipwith_l_f_xs_ys_2, cond_zipwith_l_f_xs_ys_1_3, fibs_2#1_4, zipwith_l#3_2, plus#2_2 Defined Pair Symbols: COND_ZIPWITH_L_F_XS_YS_1_3, COND_TAKE_L_N_XS_2, COND_ZIPWITH_L_F_XS_YS_2, ZIPWITH_L_F_XS_YS#1_4, PLUS#2_2 Compound Symbols: c6_1, c3_2, c3_1, c8_2, c8_1, c12_2, c12_1, c2_1, c9_1, c11_1, c5_1, c10_1 ---------------------------------------- (81) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID)) Split RHS of tuples not part of any SCC ---------------------------------------- (82) Obligation: Complexity Dependency Tuples Problem Rules: zipwith_l_f_xs_ys#1(plus, fibs, z0, z1) -> cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0) zipwith_l_f_xs_ys#1(plus, fibs_2(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3) zipwith_l_f_xs_ys#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), zipwith_l_f_xs_ys(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), fibs_2(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys_1(ConsL(z0, z1), z2, z3) -> ConsL(plus#2(z2, z0), zipwith_l#3(z3, z1)) fibs_2#1(zipwith_l, plus, tail_l, z0) -> ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))) zipwith_l#3(z0, z1) -> zipwith_l_f_xs_ys(plus, z0, z1) plus#2(0, z0) -> z0 plus#2(S(z0), z1) -> S(plus#2(z0, z1)) Tuples: COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, x1)), S(x2)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs_2(x1, x2, x3), x4)), S(x5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x1, x2, x3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4)), S(x5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, x2)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[6])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4)), x1, x2) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x0), x1, x2) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x0, x1, x2), x3), x4, x5) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x0, x1, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3), x4, x5) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3, bot[7])) COND_TAKE_L_N_XS(ConsL(x0, fibs_2(zipwith_l, plus, tail_l)), S(x1)) -> c2(COND_TAKE_L_N_XS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x1)) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0, x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x0, x1) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0)) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z1)), S(z2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z1), z2), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z1, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z2)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z2), z0, z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z2, bot[6])) PLUS#2(S(S(y0)), z1) -> c5(PLUS#2(S(y0), z1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x0)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) S tuples: COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, x2)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[6])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4)), x1, x2) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x0), x1, x2) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x0, x1, x2), x3), x4, x5) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x0, x1, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3), x4, x5) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3, bot[7])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0, x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x0, x1) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0)) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z2)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z2), z0, z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z2, bot[6])) PLUS#2(S(S(y0)), z1) -> c5(PLUS#2(S(y0), z1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x0)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) K tuples: COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(z1, z2, z3)), S(z4)) -> c3(COND_TAKE_L_N_XS(zipwith_l_f_xs_ys#1(z1, z2, z3, bot[0]), z4), ZIPWITH_L_F_XS_YS#1(z1, z2, z3, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, fibs_2(z1, z2, z3)), S(z4)) -> c2(COND_TAKE_L_N_XS(fibs_2#1(z1, z2, z3, bot[0]), z4)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x1)) Defined Rule Symbols: zipwith_l_f_xs_ys#1_4, cond_zipwith_l_f_xs_ys_2, cond_zipwith_l_f_xs_ys_1_3, fibs_2#1_4, zipwith_l#3_2, plus#2_2 Defined Pair Symbols: COND_ZIPWITH_L_F_XS_YS_1_3, COND_TAKE_L_N_XS_2, COND_ZIPWITH_L_F_XS_YS_2, ZIPWITH_L_F_XS_YS#1_4, PLUS#2_2 Compound Symbols: c6_1, c3_2, c3_1, c8_2, c8_1, c12_2, c12_1, c2_1, c9_1, c11_1, c5_1, c10_1, c_1 ---------------------------------------- (83) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1))) Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S. ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) We considered the (Usable) Rules:none And the Tuples: COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, x1)), S(x2)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs_2(x1, x2, x3), x4)), S(x5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x1, x2, x3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4)), S(x5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, x2)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[6])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4)), x1, x2) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x0), x1, x2) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x0, x1, x2), x3), x4, x5) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x0, x1, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3), x4, x5) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3, bot[7])) COND_TAKE_L_N_XS(ConsL(x0, fibs_2(zipwith_l, plus, tail_l)), S(x1)) -> c2(COND_TAKE_L_N_XS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x1)) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0, x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x0, x1) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0)) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z1)), S(z2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z1), z2), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z1, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z2)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z2), z0, z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z2, bot[6])) PLUS#2(S(S(y0)), z1) -> c5(PLUS#2(S(y0), z1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x0)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) The order we found is given by the following interpretation: Polynomial interpretation : POL(0) = 0 POL(COND_TAKE_L_N_XS(x_1, x_2)) = x_2 POL(COND_ZIPWITH_L_F_XS_YS(x_1, x_2)) = 0 POL(COND_ZIPWITH_L_F_XS_YS_1(x_1, x_2, x_3)) = 0 POL(ConsL(x_1, x_2)) = 0 POL(PLUS#2(x_1, x_2)) = 0 POL(S(x_1)) = [1] + x_1 POL(ZIPWITH_L_F_XS_YS#1(x_1, x_2, x_3, x_4)) = x_1 + x_4 POL(bot[0]) = [1] POL(bot[6]) = 0 POL(bot[7]) = 0 POL(c(x_1)) = x_1 POL(c10(x_1)) = x_1 POL(c11(x_1)) = x_1 POL(c12(x_1)) = x_1 POL(c12(x_1, x_2)) = x_1 + x_2 POL(c2(x_1)) = x_1 POL(c3(x_1)) = x_1 POL(c3(x_1, x_2)) = x_1 + x_2 POL(c5(x_1)) = x_1 POL(c6(x_1)) = x_1 POL(c8(x_1)) = x_1 POL(c8(x_1, x_2)) = x_1 + x_2 POL(c9(x_1)) = x_1 POL(cond_zipwith_l_f_xs_ys(x_1, x_2)) = 0 POL(cond_zipwith_l_f_xs_ys_1(x_1, x_2, x_3)) = 0 POL(fibs) = 0 POL(fibs_2(x_1, x_2, x_3)) = 0 POL(fibs_2#1(x_1, x_2, x_3, x_4)) = x_1 + x_2 + x_3 POL(plus) = 0 POL(plus#2(x_1, x_2)) = [1] + x_1 + x_2 POL(tail_l) = 0 POL(zipwith_l) = 0 POL(zipwith_l#3(x_1, x_2)) = 0 POL(zipwith_l_f_xs_ys(x_1, x_2, x_3)) = 0 POL(zipwith_l_f_xs_ys#1(x_1, x_2, x_3, x_4)) = x_1 + x_2 + x_3 ---------------------------------------- (84) Obligation: Complexity Dependency Tuples Problem Rules: zipwith_l_f_xs_ys#1(plus, fibs, z0, z1) -> cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0) zipwith_l_f_xs_ys#1(plus, fibs_2(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3) zipwith_l_f_xs_ys#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), zipwith_l_f_xs_ys(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), fibs_2(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys_1(ConsL(z0, z1), z2, z3) -> ConsL(plus#2(z2, z0), zipwith_l#3(z3, z1)) fibs_2#1(zipwith_l, plus, tail_l, z0) -> ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))) zipwith_l#3(z0, z1) -> zipwith_l_f_xs_ys(plus, z0, z1) plus#2(0, z0) -> z0 plus#2(S(z0), z1) -> S(plus#2(z0, z1)) Tuples: COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, x1)), S(x2)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs_2(x1, x2, x3), x4)), S(x5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x1, x2, x3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4)), S(x5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, x2)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[6])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4)), x1, x2) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x0), x1, x2) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x0, x1, x2), x3), x4, x5) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x0, x1, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3), x4, x5) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3, bot[7])) COND_TAKE_L_N_XS(ConsL(x0, fibs_2(zipwith_l, plus, tail_l)), S(x1)) -> c2(COND_TAKE_L_N_XS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x1)) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0, x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x0, x1) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0)) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z1)), S(z2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z1), z2), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z1, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z2)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z2), z0, z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z2, bot[6])) PLUS#2(S(S(y0)), z1) -> c5(PLUS#2(S(y0), z1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x0)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) S tuples: COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, x2)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[6])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4)), x1, x2) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x0), x1, x2) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x0, x1, x2), x3), x4, x5) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x0, x1, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3), x4, x5) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3, bot[7])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0, x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x0, x1) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0)) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z2)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z2), z0, z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z2, bot[6])) PLUS#2(S(S(y0)), z1) -> c5(PLUS#2(S(y0), z1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x0)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) K tuples: COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(z1, z2, z3)), S(z4)) -> c3(COND_TAKE_L_N_XS(zipwith_l_f_xs_ys#1(z1, z2, z3, bot[0]), z4), ZIPWITH_L_F_XS_YS#1(z1, z2, z3, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, fibs_2(z1, z2, z3)), S(z4)) -> c2(COND_TAKE_L_N_XS(fibs_2#1(z1, z2, z3, bot[0]), z4)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x1)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) Defined Rule Symbols: zipwith_l_f_xs_ys#1_4, cond_zipwith_l_f_xs_ys_2, cond_zipwith_l_f_xs_ys_1_3, fibs_2#1_4, zipwith_l#3_2, plus#2_2 Defined Pair Symbols: COND_ZIPWITH_L_F_XS_YS_1_3, COND_TAKE_L_N_XS_2, COND_ZIPWITH_L_F_XS_YS_2, ZIPWITH_L_F_XS_YS#1_4, PLUS#2_2 Compound Symbols: c6_1, c3_2, c3_1, c8_2, c8_1, c12_2, c12_1, c2_1, c9_1, c11_1, c5_1, c10_1, c_1 ---------------------------------------- (85) CdtInstantiationProof (BOTH BOUNDS(ID, ID)) Use instantiation to replace ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4)), x1, x2) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[7])) by ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ---------------------------------------- (86) Obligation: Complexity Dependency Tuples Problem Rules: zipwith_l_f_xs_ys#1(plus, fibs, z0, z1) -> cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0) zipwith_l_f_xs_ys#1(plus, fibs_2(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3) zipwith_l_f_xs_ys#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), zipwith_l_f_xs_ys(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), fibs_2(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys_1(ConsL(z0, z1), z2, z3) -> ConsL(plus#2(z2, z0), zipwith_l#3(z3, z1)) fibs_2#1(zipwith_l, plus, tail_l, z0) -> ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))) zipwith_l#3(z0, z1) -> zipwith_l_f_xs_ys(plus, z0, z1) plus#2(0, z0) -> z0 plus#2(S(z0), z1) -> S(plus#2(z0, z1)) Tuples: COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, x1)), S(x2)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs_2(x1, x2, x3), x4)), S(x5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x1, x2, x3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4)), S(x5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, x2)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[6])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x0), x1, x2) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x0, x1, x2), x3), x4, x5) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x0, x1, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3), x4, x5) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3, bot[7])) COND_TAKE_L_N_XS(ConsL(x0, fibs_2(zipwith_l, plus, tail_l)), S(x1)) -> c2(COND_TAKE_L_N_XS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x1)) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0, x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x0, x1) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0)) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z1)), S(z2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z1), z2), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z1, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z2)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z2), z0, z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z2, bot[6])) PLUS#2(S(S(y0)), z1) -> c5(PLUS#2(S(y0), z1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x0)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) S tuples: COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, x2)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[6])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x0), x1, x2) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x0, x1, x2), x3), x4, x5) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x0, x1, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3), x4, x5) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3, bot[7])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0, x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x0, x1) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0)) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z2)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z2), z0, z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z2, bot[6])) PLUS#2(S(S(y0)), z1) -> c5(PLUS#2(S(y0), z1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x0)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) K tuples: COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(z1, z2, z3)), S(z4)) -> c3(COND_TAKE_L_N_XS(zipwith_l_f_xs_ys#1(z1, z2, z3, bot[0]), z4), ZIPWITH_L_F_XS_YS#1(z1, z2, z3, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, fibs_2(z1, z2, z3)), S(z4)) -> c2(COND_TAKE_L_N_XS(fibs_2#1(z1, z2, z3, bot[0]), z4)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x1)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) Defined Rule Symbols: zipwith_l_f_xs_ys#1_4, cond_zipwith_l_f_xs_ys_2, cond_zipwith_l_f_xs_ys_1_3, fibs_2#1_4, zipwith_l#3_2, plus#2_2 Defined Pair Symbols: COND_ZIPWITH_L_F_XS_YS_1_3, COND_TAKE_L_N_XS_2, COND_ZIPWITH_L_F_XS_YS_2, ZIPWITH_L_F_XS_YS#1_4, PLUS#2_2 Compound Symbols: c6_1, c3_2, c3_1, c8_2, c8_1, c12_1, c12_2, c2_1, c9_1, c11_1, c5_1, c10_1, c_1 ---------------------------------------- (87) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID)) Split RHS of tuples not part of any SCC ---------------------------------------- (88) Obligation: Complexity Dependency Tuples Problem Rules: zipwith_l_f_xs_ys#1(plus, fibs, z0, z1) -> cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0) zipwith_l_f_xs_ys#1(plus, fibs_2(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3) zipwith_l_f_xs_ys#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), zipwith_l_f_xs_ys(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), fibs_2(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys_1(ConsL(z0, z1), z2, z3) -> ConsL(plus#2(z2, z0), zipwith_l#3(z3, z1)) fibs_2#1(zipwith_l, plus, tail_l, z0) -> ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))) zipwith_l#3(z0, z1) -> zipwith_l_f_xs_ys(plus, z0, z1) plus#2(0, z0) -> z0 plus#2(S(z0), z1) -> S(plus#2(z0, z1)) Tuples: COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, x1)), S(x2)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs_2(x1, x2, x3), x4)), S(x5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x1, x2, x3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4)), S(x5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, x2)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[6])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x0), x1, x2) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x0, x1, x2), x3), x4, x5) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x0, x1, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3), x4, x5) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3, bot[7])) COND_TAKE_L_N_XS(ConsL(x0, fibs_2(zipwith_l, plus, tail_l)), S(x1)) -> c2(COND_TAKE_L_N_XS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x1)) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0, x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x0, x1) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0)) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z1)), S(z2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z1), z2), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z1, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z2)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z2), z0, z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z2, bot[6])) PLUS#2(S(S(y0)), z1) -> c5(PLUS#2(S(y0), z1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x0)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) S tuples: COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, x2)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[6])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x0), x1, x2) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x0, x1, x2), x3), x4, x5) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x0, x1, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3), x4, x5) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3, bot[7])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0, x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x0, x1) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0)) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z2)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z2), z0, z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z2, bot[6])) PLUS#2(S(S(y0)), z1) -> c5(PLUS#2(S(y0), z1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x0)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) K tuples: COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(z1, z2, z3)), S(z4)) -> c3(COND_TAKE_L_N_XS(zipwith_l_f_xs_ys#1(z1, z2, z3, bot[0]), z4), ZIPWITH_L_F_XS_YS#1(z1, z2, z3, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, fibs_2(z1, z2, z3)), S(z4)) -> c2(COND_TAKE_L_N_XS(fibs_2#1(z1, z2, z3, bot[0]), z4)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x1)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) Defined Rule Symbols: zipwith_l_f_xs_ys#1_4, cond_zipwith_l_f_xs_ys_2, cond_zipwith_l_f_xs_ys_1_3, fibs_2#1_4, zipwith_l#3_2, plus#2_2 Defined Pair Symbols: COND_ZIPWITH_L_F_XS_YS_1_3, COND_TAKE_L_N_XS_2, COND_ZIPWITH_L_F_XS_YS_2, ZIPWITH_L_F_XS_YS#1_4, PLUS#2_2 Compound Symbols: c6_1, c3_2, c3_1, c8_2, c8_1, c12_1, c12_2, c2_1, c9_1, c11_1, c5_1, c10_1, c_1, c1_1 ---------------------------------------- (89) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1))) Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S. ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) We considered the (Usable) Rules:none And the Tuples: COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, x1)), S(x2)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs_2(x1, x2, x3), x4)), S(x5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x1, x2, x3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4)), S(x5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, x2)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[6])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x0), x1, x2) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x0, x1, x2), x3), x4, x5) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x0, x1, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3), x4, x5) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3, bot[7])) COND_TAKE_L_N_XS(ConsL(x0, fibs_2(zipwith_l, plus, tail_l)), S(x1)) -> c2(COND_TAKE_L_N_XS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x1)) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0, x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x0, x1) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0)) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z1)), S(z2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z1), z2), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z1, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z2)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z2), z0, z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z2, bot[6])) PLUS#2(S(S(y0)), z1) -> c5(PLUS#2(S(y0), z1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x0)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) The order we found is given by the following interpretation: Polynomial interpretation : POL(0) = 0 POL(COND_TAKE_L_N_XS(x_1, x_2)) = [1] + x_2 POL(COND_ZIPWITH_L_F_XS_YS(x_1, x_2)) = 0 POL(COND_ZIPWITH_L_F_XS_YS_1(x_1, x_2, x_3)) = 0 POL(ConsL(x_1, x_2)) = 0 POL(PLUS#2(x_1, x_2)) = 0 POL(S(x_1)) = [1] + x_1 POL(ZIPWITH_L_F_XS_YS#1(x_1, x_2, x_3, x_4)) = x_1 + x_4 POL(bot[0]) = [1] POL(bot[6]) = 0 POL(bot[7]) = 0 POL(c(x_1)) = x_1 POL(c1(x_1)) = x_1 POL(c10(x_1)) = x_1 POL(c11(x_1)) = x_1 POL(c12(x_1)) = x_1 POL(c12(x_1, x_2)) = x_1 + x_2 POL(c2(x_1)) = x_1 POL(c3(x_1)) = x_1 POL(c3(x_1, x_2)) = x_1 + x_2 POL(c5(x_1)) = x_1 POL(c6(x_1)) = x_1 POL(c8(x_1)) = x_1 POL(c8(x_1, x_2)) = x_1 + x_2 POL(c9(x_1)) = x_1 POL(cond_zipwith_l_f_xs_ys(x_1, x_2)) = 0 POL(cond_zipwith_l_f_xs_ys_1(x_1, x_2, x_3)) = 0 POL(fibs) = 0 POL(fibs_2(x_1, x_2, x_3)) = 0 POL(fibs_2#1(x_1, x_2, x_3, x_4)) = x_1 + x_2 + x_3 POL(plus) = 0 POL(plus#2(x_1, x_2)) = [1] + x_1 + x_2 POL(tail_l) = 0 POL(zipwith_l) = 0 POL(zipwith_l#3(x_1, x_2)) = 0 POL(zipwith_l_f_xs_ys(x_1, x_2, x_3)) = 0 POL(zipwith_l_f_xs_ys#1(x_1, x_2, x_3, x_4)) = x_1 + x_2 + x_3 ---------------------------------------- (90) Obligation: Complexity Dependency Tuples Problem Rules: zipwith_l_f_xs_ys#1(plus, fibs, z0, z1) -> cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0) zipwith_l_f_xs_ys#1(plus, fibs_2(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3) zipwith_l_f_xs_ys#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), zipwith_l_f_xs_ys(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), fibs_2(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys_1(ConsL(z0, z1), z2, z3) -> ConsL(plus#2(z2, z0), zipwith_l#3(z3, z1)) fibs_2#1(zipwith_l, plus, tail_l, z0) -> ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))) zipwith_l#3(z0, z1) -> zipwith_l_f_xs_ys(plus, z0, z1) plus#2(0, z0) -> z0 plus#2(S(z0), z1) -> S(plus#2(z0, z1)) Tuples: COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, x1)), S(x2)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs_2(x1, x2, x3), x4)), S(x5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x1, x2, x3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4)), S(x5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, x2)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[6])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x0), x1, x2) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x0, x1, x2), x3), x4, x5) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x0, x1, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3), x4, x5) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3, bot[7])) COND_TAKE_L_N_XS(ConsL(x0, fibs_2(zipwith_l, plus, tail_l)), S(x1)) -> c2(COND_TAKE_L_N_XS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x1)) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0, x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x0, x1) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0)) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z1)), S(z2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z1), z2), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z1, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z2)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z2), z0, z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z2, bot[6])) PLUS#2(S(S(y0)), z1) -> c5(PLUS#2(S(y0), z1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x0)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) S tuples: COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, x2)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[6])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x0), x1, x2) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x0, x1, x2), x3), x4, x5) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x0, x1, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3), x4, x5) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3, bot[7])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0, x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x0, x1) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0)) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z2)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z2), z0, z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z2, bot[6])) PLUS#2(S(S(y0)), z1) -> c5(PLUS#2(S(y0), z1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x0)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) K tuples: COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(z1, z2, z3)), S(z4)) -> c3(COND_TAKE_L_N_XS(zipwith_l_f_xs_ys#1(z1, z2, z3, bot[0]), z4), ZIPWITH_L_F_XS_YS#1(z1, z2, z3, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, fibs_2(z1, z2, z3)), S(z4)) -> c2(COND_TAKE_L_N_XS(fibs_2#1(z1, z2, z3, bot[0]), z4)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x1)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) Defined Rule Symbols: zipwith_l_f_xs_ys#1_4, cond_zipwith_l_f_xs_ys_2, cond_zipwith_l_f_xs_ys_1_3, fibs_2#1_4, zipwith_l#3_2, plus#2_2 Defined Pair Symbols: COND_ZIPWITH_L_F_XS_YS_1_3, COND_TAKE_L_N_XS_2, COND_ZIPWITH_L_F_XS_YS_2, ZIPWITH_L_F_XS_YS#1_4, PLUS#2_2 Compound Symbols: c6_1, c3_2, c3_1, c8_2, c8_1, c12_1, c12_2, c2_1, c9_1, c11_1, c5_1, c10_1, c_1, c1_1 ---------------------------------------- (91) CdtInstantiationProof (BOTH BOUNDS(ID, ID)) Use instantiation to replace ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x0), x1, x2) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7])) by ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x1), x2, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x0), x1, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7])) ---------------------------------------- (92) Obligation: Complexity Dependency Tuples Problem Rules: zipwith_l_f_xs_ys#1(plus, fibs, z0, z1) -> cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0) zipwith_l_f_xs_ys#1(plus, fibs_2(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3) zipwith_l_f_xs_ys#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), zipwith_l_f_xs_ys(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), fibs_2(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys_1(ConsL(z0, z1), z2, z3) -> ConsL(plus#2(z2, z0), zipwith_l#3(z3, z1)) fibs_2#1(zipwith_l, plus, tail_l, z0) -> ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))) zipwith_l#3(z0, z1) -> zipwith_l_f_xs_ys(plus, z0, z1) plus#2(0, z0) -> z0 plus#2(S(z0), z1) -> S(plus#2(z0, z1)) Tuples: COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, x1)), S(x2)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs_2(x1, x2, x3), x4)), S(x5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x1, x2, x3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4)), S(x5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, x2)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[6])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x0, x1, x2), x3), x4, x5) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x0, x1, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3), x4, x5) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3, bot[7])) COND_TAKE_L_N_XS(ConsL(x0, fibs_2(zipwith_l, plus, tail_l)), S(x1)) -> c2(COND_TAKE_L_N_XS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x1)) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0, x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x0, x1) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0)) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z1)), S(z2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z1), z2), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z1, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z2)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z2), z0, z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z2, bot[6])) PLUS#2(S(S(y0)), z1) -> c5(PLUS#2(S(y0), z1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x0)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x1), x2, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x0), x1, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7])) S tuples: COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, x2)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[6])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x0, x1, x2), x3), x4, x5) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x0, x1, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3), x4, x5) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3, bot[7])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0, x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x0, x1) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0)) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z2)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z2), z0, z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z2, bot[6])) PLUS#2(S(S(y0)), z1) -> c5(PLUS#2(S(y0), z1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x0)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x1), x2, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x0), x1, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7])) K tuples: COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(z1, z2, z3)), S(z4)) -> c3(COND_TAKE_L_N_XS(zipwith_l_f_xs_ys#1(z1, z2, z3, bot[0]), z4), ZIPWITH_L_F_XS_YS#1(z1, z2, z3, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, fibs_2(z1, z2, z3)), S(z4)) -> c2(COND_TAKE_L_N_XS(fibs_2#1(z1, z2, z3, bot[0]), z4)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x1)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) Defined Rule Symbols: zipwith_l_f_xs_ys#1_4, cond_zipwith_l_f_xs_ys_2, cond_zipwith_l_f_xs_ys_1_3, fibs_2#1_4, zipwith_l#3_2, plus#2_2 Defined Pair Symbols: COND_ZIPWITH_L_F_XS_YS_1_3, COND_TAKE_L_N_XS_2, COND_ZIPWITH_L_F_XS_YS_2, ZIPWITH_L_F_XS_YS#1_4, PLUS#2_2 Compound Symbols: c6_1, c3_2, c3_1, c8_2, c8_1, c12_2, c12_1, c2_1, c9_1, c11_1, c5_1, c10_1, c_1, c1_1 ---------------------------------------- (93) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1))) Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S. ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x1), x2, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[7])) We considered the (Usable) Rules:none And the Tuples: COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, x1)), S(x2)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs_2(x1, x2, x3), x4)), S(x5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x1, x2, x3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4)), S(x5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, x2)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[6])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x0, x1, x2), x3), x4, x5) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x0, x1, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3), x4, x5) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3, bot[7])) COND_TAKE_L_N_XS(ConsL(x0, fibs_2(zipwith_l, plus, tail_l)), S(x1)) -> c2(COND_TAKE_L_N_XS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x1)) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0, x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x0, x1) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0)) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z1)), S(z2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z1), z2), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z1, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z2)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z2), z0, z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z2, bot[6])) PLUS#2(S(S(y0)), z1) -> c5(PLUS#2(S(y0), z1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x0)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x1), x2, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x0), x1, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7])) The order we found is given by the following interpretation: Polynomial interpretation : POL(0) = 0 POL(COND_TAKE_L_N_XS(x_1, x_2)) = [1] + x_2 POL(COND_ZIPWITH_L_F_XS_YS(x_1, x_2)) = 0 POL(COND_ZIPWITH_L_F_XS_YS_1(x_1, x_2, x_3)) = 0 POL(ConsL(x_1, x_2)) = 0 POL(PLUS#2(x_1, x_2)) = 0 POL(S(x_1)) = [1] + x_1 POL(ZIPWITH_L_F_XS_YS#1(x_1, x_2, x_3, x_4)) = x_4 POL(bot[0]) = [1] POL(bot[6]) = 0 POL(bot[7]) = 0 POL(c(x_1)) = x_1 POL(c1(x_1)) = x_1 POL(c10(x_1)) = x_1 POL(c11(x_1)) = x_1 POL(c12(x_1)) = x_1 POL(c12(x_1, x_2)) = x_1 + x_2 POL(c2(x_1)) = x_1 POL(c3(x_1)) = x_1 POL(c3(x_1, x_2)) = x_1 + x_2 POL(c5(x_1)) = x_1 POL(c6(x_1)) = x_1 POL(c8(x_1)) = x_1 POL(c8(x_1, x_2)) = x_1 + x_2 POL(c9(x_1)) = x_1 POL(cond_zipwith_l_f_xs_ys(x_1, x_2)) = 0 POL(cond_zipwith_l_f_xs_ys_1(x_1, x_2, x_3)) = 0 POL(fibs) = 0 POL(fibs_2(x_1, x_2, x_3)) = 0 POL(fibs_2#1(x_1, x_2, x_3, x_4)) = x_1 + x_2 + x_3 POL(plus) = [1] POL(plus#2(x_1, x_2)) = [1] + x_1 + x_2 POL(tail_l) = [1] POL(zipwith_l) = 0 POL(zipwith_l#3(x_1, x_2)) = 0 POL(zipwith_l_f_xs_ys(x_1, x_2, x_3)) = 0 POL(zipwith_l_f_xs_ys#1(x_1, x_2, x_3, x_4)) = x_1 + x_2 + x_3 ---------------------------------------- (94) Obligation: Complexity Dependency Tuples Problem Rules: zipwith_l_f_xs_ys#1(plus, fibs, z0, z1) -> cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0) zipwith_l_f_xs_ys#1(plus, fibs_2(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3) zipwith_l_f_xs_ys#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), zipwith_l_f_xs_ys(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), fibs_2(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys_1(ConsL(z0, z1), z2, z3) -> ConsL(plus#2(z2, z0), zipwith_l#3(z3, z1)) fibs_2#1(zipwith_l, plus, tail_l, z0) -> ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))) zipwith_l#3(z0, z1) -> zipwith_l_f_xs_ys(plus, z0, z1) plus#2(0, z0) -> z0 plus#2(S(z0), z1) -> S(plus#2(z0, z1)) Tuples: COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, x1)), S(x2)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs_2(x1, x2, x3), x4)), S(x5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x1, x2, x3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4)), S(x5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, x2)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[6])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x0, x1, x2), x3), x4, x5) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x0, x1, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3), x4, x5) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3, bot[7])) COND_TAKE_L_N_XS(ConsL(x0, fibs_2(zipwith_l, plus, tail_l)), S(x1)) -> c2(COND_TAKE_L_N_XS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x1)) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0, x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x0, x1) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0)) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z1)), S(z2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z1), z2), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z1, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z2)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z2), z0, z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z2, bot[6])) PLUS#2(S(S(y0)), z1) -> c5(PLUS#2(S(y0), z1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x0)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x1), x2, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x0), x1, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7])) S tuples: COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, x2)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[6])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x0, x1, x2), x3), x4, x5) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x0, x1, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3), x4, x5) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3, bot[7])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0, x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x0, x1) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0)) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z2)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z2), z0, z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z2, bot[6])) PLUS#2(S(S(y0)), z1) -> c5(PLUS#2(S(y0), z1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x0)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x0), x1, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7])) K tuples: COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(z1, z2, z3)), S(z4)) -> c3(COND_TAKE_L_N_XS(zipwith_l_f_xs_ys#1(z1, z2, z3, bot[0]), z4), ZIPWITH_L_F_XS_YS#1(z1, z2, z3, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, fibs_2(z1, z2, z3)), S(z4)) -> c2(COND_TAKE_L_N_XS(fibs_2#1(z1, z2, z3, bot[0]), z4)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x1)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x1), x2, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[7])) Defined Rule Symbols: zipwith_l_f_xs_ys#1_4, cond_zipwith_l_f_xs_ys_2, cond_zipwith_l_f_xs_ys_1_3, fibs_2#1_4, zipwith_l#3_2, plus#2_2 Defined Pair Symbols: COND_ZIPWITH_L_F_XS_YS_1_3, COND_TAKE_L_N_XS_2, COND_ZIPWITH_L_F_XS_YS_2, ZIPWITH_L_F_XS_YS#1_4, PLUS#2_2 Compound Symbols: c6_1, c3_2, c3_1, c8_2, c8_1, c12_2, c12_1, c2_1, c9_1, c11_1, c5_1, c10_1, c_1, c1_1 ---------------------------------------- (95) CdtInstantiationProof (BOTH BOUNDS(ID, ID)) Use instantiation to replace ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, bot[7])) by ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, bot[7])) ---------------------------------------- (96) Obligation: Complexity Dependency Tuples Problem Rules: zipwith_l_f_xs_ys#1(plus, fibs, z0, z1) -> cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0) zipwith_l_f_xs_ys#1(plus, fibs_2(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3) zipwith_l_f_xs_ys#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), zipwith_l_f_xs_ys(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), fibs_2(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys_1(ConsL(z0, z1), z2, z3) -> ConsL(plus#2(z2, z0), zipwith_l#3(z3, z1)) fibs_2#1(zipwith_l, plus, tail_l, z0) -> ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))) zipwith_l#3(z0, z1) -> zipwith_l_f_xs_ys(plus, z0, z1) plus#2(0, z0) -> z0 plus#2(S(z0), z1) -> S(plus#2(z0, z1)) Tuples: COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, x1)), S(x2)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs_2(x1, x2, x3), x4)), S(x5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x1, x2, x3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4)), S(x5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, x2)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[6])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x0, x1, x2), x3), x4, x5) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x0, x1, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3), x4, x5) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3, bot[7])) COND_TAKE_L_N_XS(ConsL(x0, fibs_2(zipwith_l, plus, tail_l)), S(x1)) -> c2(COND_TAKE_L_N_XS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x1)) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0, x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x0, x1) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0)) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z1)), S(z2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z1), z2), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z1, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z2)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z2), z0, z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z2, bot[6])) PLUS#2(S(S(y0)), z1) -> c5(PLUS#2(S(y0), z1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x0)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x1), x2, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x0), x1, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, bot[7])) S tuples: COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, x2)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[6])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x0, x1, x2), x3), x4, x5) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x0, x1, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3), x4, x5) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3, bot[7])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0, x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x0, x1) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0)) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z2)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z2), z0, z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z2, bot[6])) PLUS#2(S(S(y0)), z1) -> c5(PLUS#2(S(y0), z1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x0)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x0), x1, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, bot[7])) K tuples: COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(z1, z2, z3)), S(z4)) -> c3(COND_TAKE_L_N_XS(zipwith_l_f_xs_ys#1(z1, z2, z3, bot[0]), z4), ZIPWITH_L_F_XS_YS#1(z1, z2, z3, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, fibs_2(z1, z2, z3)), S(z4)) -> c2(COND_TAKE_L_N_XS(fibs_2#1(z1, z2, z3, bot[0]), z4)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x1)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x1), x2, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[7])) Defined Rule Symbols: zipwith_l_f_xs_ys#1_4, cond_zipwith_l_f_xs_ys_2, cond_zipwith_l_f_xs_ys_1_3, fibs_2#1_4, zipwith_l#3_2, plus#2_2 Defined Pair Symbols: COND_ZIPWITH_L_F_XS_YS_1_3, COND_TAKE_L_N_XS_2, COND_ZIPWITH_L_F_XS_YS_2, ZIPWITH_L_F_XS_YS#1_4, PLUS#2_2 Compound Symbols: c6_1, c3_2, c3_1, c8_2, c8_1, c12_1, c12_2, c2_1, c9_1, c11_1, c5_1, c10_1, c_1, c1_1 ---------------------------------------- (97) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID)) Split RHS of tuples not part of any SCC ---------------------------------------- (98) Obligation: Complexity Dependency Tuples Problem Rules: zipwith_l_f_xs_ys#1(plus, fibs, z0, z1) -> cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0) zipwith_l_f_xs_ys#1(plus, fibs_2(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3) zipwith_l_f_xs_ys#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), zipwith_l_f_xs_ys(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), fibs_2(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys_1(ConsL(z0, z1), z2, z3) -> ConsL(plus#2(z2, z0), zipwith_l#3(z3, z1)) fibs_2#1(zipwith_l, plus, tail_l, z0) -> ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))) zipwith_l#3(z0, z1) -> zipwith_l_f_xs_ys(plus, z0, z1) plus#2(0, z0) -> z0 plus#2(S(z0), z1) -> S(plus#2(z0, z1)) Tuples: COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, x1)), S(x2)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs_2(x1, x2, x3), x4)), S(x5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x1, x2, x3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4)), S(x5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, x2)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[6])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x0, x1, x2), x3), x4, x5) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x0, x1, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3), x4, x5) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3, bot[7])) COND_TAKE_L_N_XS(ConsL(x0, fibs_2(zipwith_l, plus, tail_l)), S(x1)) -> c2(COND_TAKE_L_N_XS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x1)) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0, x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x0, x1) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0)) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z1)), S(z2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z1), z2), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z1, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z2)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z2), z0, z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z2, bot[6])) PLUS#2(S(S(y0)), z1) -> c5(PLUS#2(S(y0), z1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x0)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x1), x2, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x0), x1, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[7])) S tuples: COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, x2)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[6])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x0, x1, x2), x3), x4, x5) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x0, x1, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3), x4, x5) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3, bot[7])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0, x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x0, x1) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0)) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z2)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z2), z0, z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z2, bot[6])) PLUS#2(S(S(y0)), z1) -> c5(PLUS#2(S(y0), z1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x0)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x0), x1, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[7])) K tuples: COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(z1, z2, z3)), S(z4)) -> c3(COND_TAKE_L_N_XS(zipwith_l_f_xs_ys#1(z1, z2, z3, bot[0]), z4), ZIPWITH_L_F_XS_YS#1(z1, z2, z3, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, fibs_2(z1, z2, z3)), S(z4)) -> c2(COND_TAKE_L_N_XS(fibs_2#1(z1, z2, z3, bot[0]), z4)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x1)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x1), x2, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[7])) Defined Rule Symbols: zipwith_l_f_xs_ys#1_4, cond_zipwith_l_f_xs_ys_2, cond_zipwith_l_f_xs_ys_1_3, fibs_2#1_4, zipwith_l#3_2, plus#2_2 Defined Pair Symbols: COND_ZIPWITH_L_F_XS_YS_1_3, COND_TAKE_L_N_XS_2, COND_ZIPWITH_L_F_XS_YS_2, ZIPWITH_L_F_XS_YS#1_4, PLUS#2_2 Compound Symbols: c6_1, c3_2, c3_1, c8_2, c8_1, c12_1, c12_2, c2_1, c9_1, c11_1, c5_1, c10_1, c_1, c1_1, c4_1 ---------------------------------------- (99) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1))) Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S. ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[7])) We considered the (Usable) Rules:none And the Tuples: COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, x1)), S(x2)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs_2(x1, x2, x3), x4)), S(x5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x1, x2, x3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4)), S(x5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, x2)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[6])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x0, x1, x2), x3), x4, x5) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x0, x1, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3), x4, x5) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3, bot[7])) COND_TAKE_L_N_XS(ConsL(x0, fibs_2(zipwith_l, plus, tail_l)), S(x1)) -> c2(COND_TAKE_L_N_XS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x1)) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0, x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x0, x1) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0)) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z1)), S(z2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z1), z2), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z1, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z2)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z2), z0, z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z2, bot[6])) PLUS#2(S(S(y0)), z1) -> c5(PLUS#2(S(y0), z1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x0)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x1), x2, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x0), x1, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[7])) The order we found is given by the following interpretation: Polynomial interpretation : POL(0) = 0 POL(COND_TAKE_L_N_XS(x_1, x_2)) = x_2 POL(COND_ZIPWITH_L_F_XS_YS(x_1, x_2)) = 0 POL(COND_ZIPWITH_L_F_XS_YS_1(x_1, x_2, x_3)) = 0 POL(ConsL(x_1, x_2)) = 0 POL(PLUS#2(x_1, x_2)) = 0 POL(S(x_1)) = [1] + x_1 POL(ZIPWITH_L_F_XS_YS#1(x_1, x_2, x_3, x_4)) = x_1 + x_4 POL(bot[0]) = [1] POL(bot[6]) = 0 POL(bot[7]) = 0 POL(c(x_1)) = x_1 POL(c1(x_1)) = x_1 POL(c10(x_1)) = x_1 POL(c11(x_1)) = x_1 POL(c12(x_1)) = x_1 POL(c12(x_1, x_2)) = x_1 + x_2 POL(c2(x_1)) = x_1 POL(c3(x_1)) = x_1 POL(c3(x_1, x_2)) = x_1 + x_2 POL(c4(x_1)) = x_1 POL(c5(x_1)) = x_1 POL(c6(x_1)) = x_1 POL(c8(x_1)) = x_1 POL(c8(x_1, x_2)) = x_1 + x_2 POL(c9(x_1)) = x_1 POL(cond_zipwith_l_f_xs_ys(x_1, x_2)) = 0 POL(cond_zipwith_l_f_xs_ys_1(x_1, x_2, x_3)) = 0 POL(fibs) = 0 POL(fibs_2(x_1, x_2, x_3)) = 0 POL(fibs_2#1(x_1, x_2, x_3, x_4)) = x_1 + x_2 + x_3 POL(plus) = 0 POL(plus#2(x_1, x_2)) = [1] + x_1 + x_2 POL(tail_l) = 0 POL(zipwith_l) = 0 POL(zipwith_l#3(x_1, x_2)) = 0 POL(zipwith_l_f_xs_ys(x_1, x_2, x_3)) = 0 POL(zipwith_l_f_xs_ys#1(x_1, x_2, x_3, x_4)) = x_1 + x_2 + x_3 ---------------------------------------- (100) Obligation: Complexity Dependency Tuples Problem Rules: zipwith_l_f_xs_ys#1(plus, fibs, z0, z1) -> cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0) zipwith_l_f_xs_ys#1(plus, fibs_2(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3) zipwith_l_f_xs_ys#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), zipwith_l_f_xs_ys(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), fibs_2(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys_1(ConsL(z0, z1), z2, z3) -> ConsL(plus#2(z2, z0), zipwith_l#3(z3, z1)) fibs_2#1(zipwith_l, plus, tail_l, z0) -> ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))) zipwith_l#3(z0, z1) -> zipwith_l_f_xs_ys(plus, z0, z1) plus#2(0, z0) -> z0 plus#2(S(z0), z1) -> S(plus#2(z0, z1)) Tuples: COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, x1)), S(x2)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs_2(x1, x2, x3), x4)), S(x5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x1, x2, x3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4)), S(x5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, x2)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[6])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x0, x1, x2), x3), x4, x5) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x0, x1, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3), x4, x5) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3, bot[7])) COND_TAKE_L_N_XS(ConsL(x0, fibs_2(zipwith_l, plus, tail_l)), S(x1)) -> c2(COND_TAKE_L_N_XS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x1)) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0, x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x0, x1) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0)) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z1)), S(z2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z1), z2), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z1, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z2)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z2), z0, z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z2, bot[6])) PLUS#2(S(S(y0)), z1) -> c5(PLUS#2(S(y0), z1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x0)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x1), x2, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x0), x1, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[7])) S tuples: COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, x2)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[6])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x0, x1, x2), x3), x4, x5) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x0, x1, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3), x4, x5) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3, bot[7])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0, x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x0, x1) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0)) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z2)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z2), z0, z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z2, bot[6])) PLUS#2(S(S(y0)), z1) -> c5(PLUS#2(S(y0), z1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x0)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x0), x1, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, bot[7])) K tuples: COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(z1, z2, z3)), S(z4)) -> c3(COND_TAKE_L_N_XS(zipwith_l_f_xs_ys#1(z1, z2, z3, bot[0]), z4), ZIPWITH_L_F_XS_YS#1(z1, z2, z3, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, fibs_2(z1, z2, z3)), S(z4)) -> c2(COND_TAKE_L_N_XS(fibs_2#1(z1, z2, z3, bot[0]), z4)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x1)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x1), x2, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[7])) Defined Rule Symbols: zipwith_l_f_xs_ys#1_4, cond_zipwith_l_f_xs_ys_2, cond_zipwith_l_f_xs_ys_1_3, fibs_2#1_4, zipwith_l#3_2, plus#2_2 Defined Pair Symbols: COND_ZIPWITH_L_F_XS_YS_1_3, COND_TAKE_L_N_XS_2, COND_ZIPWITH_L_F_XS_YS_2, ZIPWITH_L_F_XS_YS#1_4, PLUS#2_2 Compound Symbols: c6_1, c3_2, c3_1, c8_2, c8_1, c12_1, c12_2, c2_1, c9_1, c11_1, c5_1, c10_1, c_1, c1_1, c4_1 ---------------------------------------- (101) CdtInstantiationProof (BOTH BOUNDS(ID, ID)) Use instantiation to replace ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x0, x1, x2), x3), x4, x5) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x0, x1, x2), x3, bot[7])) by ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x1, x2, x3), x4), x5, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x1, x2, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5), x6, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x0, x1, x2), x3), x4, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x0, x1, x2), x3, bot[7])) ---------------------------------------- (102) Obligation: Complexity Dependency Tuples Problem Rules: zipwith_l_f_xs_ys#1(plus, fibs, z0, z1) -> cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0) zipwith_l_f_xs_ys#1(plus, fibs_2(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3) zipwith_l_f_xs_ys#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), zipwith_l_f_xs_ys(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), fibs_2(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys_1(ConsL(z0, z1), z2, z3) -> ConsL(plus#2(z2, z0), zipwith_l#3(z3, z1)) fibs_2#1(zipwith_l, plus, tail_l, z0) -> ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))) zipwith_l#3(z0, z1) -> zipwith_l_f_xs_ys(plus, z0, z1) plus#2(0, z0) -> z0 plus#2(S(z0), z1) -> S(plus#2(z0, z1)) Tuples: COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, x1)), S(x2)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs_2(x1, x2, x3), x4)), S(x5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x1, x2, x3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4)), S(x5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, x2)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[6])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3), x4, x5) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3, bot[7])) COND_TAKE_L_N_XS(ConsL(x0, fibs_2(zipwith_l, plus, tail_l)), S(x1)) -> c2(COND_TAKE_L_N_XS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x1)) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0, x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x0, x1) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0)) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z1)), S(z2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z1), z2), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z1, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z2)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z2), z0, z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z2, bot[6])) PLUS#2(S(S(y0)), z1) -> c5(PLUS#2(S(y0), z1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x0)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x1), x2, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x0), x1, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x1, x2, x3), x4), x5, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x1, x2, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5), x6, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x0, x1, x2), x3), x4, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x0, x1, x2), x3, bot[7])) S tuples: COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, x2)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[6])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3), x4, x5) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3, bot[7])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0, x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x0, x1) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0)) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z2)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z2), z0, z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z2, bot[6])) PLUS#2(S(S(y0)), z1) -> c5(PLUS#2(S(y0), z1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x0)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x0), x1, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x1, x2, x3), x4), x5, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x1, x2, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5), x6, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x0, x1, x2), x3), x4, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x0, x1, x2), x3, bot[7])) K tuples: COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(z1, z2, z3)), S(z4)) -> c3(COND_TAKE_L_N_XS(zipwith_l_f_xs_ys#1(z1, z2, z3, bot[0]), z4), ZIPWITH_L_F_XS_YS#1(z1, z2, z3, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, fibs_2(z1, z2, z3)), S(z4)) -> c2(COND_TAKE_L_N_XS(fibs_2#1(z1, z2, z3, bot[0]), z4)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x1)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x1), x2, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[7])) Defined Rule Symbols: zipwith_l_f_xs_ys#1_4, cond_zipwith_l_f_xs_ys_2, cond_zipwith_l_f_xs_ys_1_3, fibs_2#1_4, zipwith_l#3_2, plus#2_2 Defined Pair Symbols: COND_ZIPWITH_L_F_XS_YS_1_3, COND_TAKE_L_N_XS_2, COND_ZIPWITH_L_F_XS_YS_2, ZIPWITH_L_F_XS_YS#1_4, PLUS#2_2 Compound Symbols: c6_1, c3_2, c3_1, c8_2, c8_1, c12_2, c12_1, c2_1, c9_1, c11_1, c5_1, c10_1, c_1, c1_1, c4_1 ---------------------------------------- (103) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1))) Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S. ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x1, x2, x3), x4), x5, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x1, x2, x3), x4, bot[7])) We considered the (Usable) Rules:none And the Tuples: COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, x1)), S(x2)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs_2(x1, x2, x3), x4)), S(x5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x1, x2, x3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4)), S(x5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, x2)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[6])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3), x4, x5) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3, bot[7])) COND_TAKE_L_N_XS(ConsL(x0, fibs_2(zipwith_l, plus, tail_l)), S(x1)) -> c2(COND_TAKE_L_N_XS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x1)) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0, x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x0, x1) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0)) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z1)), S(z2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z1), z2), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z1, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z2)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z2), z0, z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z2, bot[6])) PLUS#2(S(S(y0)), z1) -> c5(PLUS#2(S(y0), z1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x0)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x1), x2, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x0), x1, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x1, x2, x3), x4), x5, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x1, x2, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5), x6, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x0, x1, x2), x3), x4, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x0, x1, x2), x3, bot[7])) The order we found is given by the following interpretation: Polynomial interpretation : POL(0) = 0 POL(COND_TAKE_L_N_XS(x_1, x_2)) = x_2 POL(COND_ZIPWITH_L_F_XS_YS(x_1, x_2)) = 0 POL(COND_ZIPWITH_L_F_XS_YS_1(x_1, x_2, x_3)) = 0 POL(ConsL(x_1, x_2)) = 0 POL(PLUS#2(x_1, x_2)) = 0 POL(S(x_1)) = [1] + x_1 POL(ZIPWITH_L_F_XS_YS#1(x_1, x_2, x_3, x_4)) = x_1 + x_4 POL(bot[0]) = [1] POL(bot[6]) = 0 POL(bot[7]) = 0 POL(c(x_1)) = x_1 POL(c1(x_1)) = x_1 POL(c10(x_1)) = x_1 POL(c11(x_1)) = x_1 POL(c12(x_1)) = x_1 POL(c12(x_1, x_2)) = x_1 + x_2 POL(c2(x_1)) = x_1 POL(c3(x_1)) = x_1 POL(c3(x_1, x_2)) = x_1 + x_2 POL(c4(x_1)) = x_1 POL(c5(x_1)) = x_1 POL(c6(x_1)) = x_1 POL(c8(x_1)) = x_1 POL(c8(x_1, x_2)) = x_1 + x_2 POL(c9(x_1)) = x_1 POL(cond_zipwith_l_f_xs_ys(x_1, x_2)) = 0 POL(cond_zipwith_l_f_xs_ys_1(x_1, x_2, x_3)) = 0 POL(fibs) = 0 POL(fibs_2(x_1, x_2, x_3)) = 0 POL(fibs_2#1(x_1, x_2, x_3, x_4)) = x_1 + x_2 + x_3 POL(plus) = 0 POL(plus#2(x_1, x_2)) = [1] + x_1 + x_2 POL(tail_l) = 0 POL(zipwith_l) = 0 POL(zipwith_l#3(x_1, x_2)) = 0 POL(zipwith_l_f_xs_ys(x_1, x_2, x_3)) = 0 POL(zipwith_l_f_xs_ys#1(x_1, x_2, x_3, x_4)) = x_1 + x_2 + x_3 ---------------------------------------- (104) Obligation: Complexity Dependency Tuples Problem Rules: zipwith_l_f_xs_ys#1(plus, fibs, z0, z1) -> cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0) zipwith_l_f_xs_ys#1(plus, fibs_2(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3) zipwith_l_f_xs_ys#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), zipwith_l_f_xs_ys(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), fibs_2(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys_1(ConsL(z0, z1), z2, z3) -> ConsL(plus#2(z2, z0), zipwith_l#3(z3, z1)) fibs_2#1(zipwith_l, plus, tail_l, z0) -> ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))) zipwith_l#3(z0, z1) -> zipwith_l_f_xs_ys(plus, z0, z1) plus#2(0, z0) -> z0 plus#2(S(z0), z1) -> S(plus#2(z0, z1)) Tuples: COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, x1)), S(x2)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs_2(x1, x2, x3), x4)), S(x5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x1, x2, x3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4)), S(x5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, x2)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[6])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3), x4, x5) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3, bot[7])) COND_TAKE_L_N_XS(ConsL(x0, fibs_2(zipwith_l, plus, tail_l)), S(x1)) -> c2(COND_TAKE_L_N_XS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x1)) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0, x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x0, x1) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0)) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z1)), S(z2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z1), z2), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z1, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z2)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z2), z0, z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z2, bot[6])) PLUS#2(S(S(y0)), z1) -> c5(PLUS#2(S(y0), z1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x0)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x1), x2, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x0), x1, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x1, x2, x3), x4), x5, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x1, x2, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5), x6, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x0, x1, x2), x3), x4, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x0, x1, x2), x3, bot[7])) S tuples: COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, x2)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[6])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3), x4, x5) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3, bot[7])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0, x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x0, x1) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0)) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z2)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z2), z0, z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z2, bot[6])) PLUS#2(S(S(y0)), z1) -> c5(PLUS#2(S(y0), z1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x0)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x0), x1, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5), x6, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x0, x1, x2), x3), x4, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x0, x1, x2), x3, bot[7])) K tuples: COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(z1, z2, z3)), S(z4)) -> c3(COND_TAKE_L_N_XS(zipwith_l_f_xs_ys#1(z1, z2, z3, bot[0]), z4), ZIPWITH_L_F_XS_YS#1(z1, z2, z3, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, fibs_2(z1, z2, z3)), S(z4)) -> c2(COND_TAKE_L_N_XS(fibs_2#1(z1, z2, z3, bot[0]), z4)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x1)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x1), x2, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x1, x2, x3), x4), x5, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x1, x2, x3), x4, bot[7])) Defined Rule Symbols: zipwith_l_f_xs_ys#1_4, cond_zipwith_l_f_xs_ys_2, cond_zipwith_l_f_xs_ys_1_3, fibs_2#1_4, zipwith_l#3_2, plus#2_2 Defined Pair Symbols: COND_ZIPWITH_L_F_XS_YS_1_3, COND_TAKE_L_N_XS_2, COND_ZIPWITH_L_F_XS_YS_2, ZIPWITH_L_F_XS_YS#1_4, PLUS#2_2 Compound Symbols: c6_1, c3_2, c3_1, c8_2, c8_1, c12_2, c12_1, c2_1, c9_1, c11_1, c5_1, c10_1, c_1, c1_1, c4_1 ---------------------------------------- (105) CdtInstantiationProof (BOTH BOUNDS(ID, ID)) Use instantiation to replace ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x3, bot[7])) by ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4), x5, bot[0]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[7])) ---------------------------------------- (106) Obligation: Complexity Dependency Tuples Problem Rules: zipwith_l_f_xs_ys#1(plus, fibs, z0, z1) -> cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0) zipwith_l_f_xs_ys#1(plus, fibs_2(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3) zipwith_l_f_xs_ys#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), zipwith_l_f_xs_ys(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), fibs_2(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys_1(ConsL(z0, z1), z2, z3) -> ConsL(plus#2(z2, z0), zipwith_l#3(z3, z1)) fibs_2#1(zipwith_l, plus, tail_l, z0) -> ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))) zipwith_l#3(z0, z1) -> zipwith_l_f_xs_ys(plus, z0, z1) plus#2(0, z0) -> z0 plus#2(S(z0), z1) -> S(plus#2(z0, z1)) Tuples: COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, x1)), S(x2)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs_2(x1, x2, x3), x4)), S(x5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x1, x2, x3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4)), S(x5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, x2)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[6])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3), x4, x5) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3, bot[7])) COND_TAKE_L_N_XS(ConsL(x0, fibs_2(zipwith_l, plus, tail_l)), S(x1)) -> c2(COND_TAKE_L_N_XS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x1)) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0, x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x0, x1) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0)) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z1)), S(z2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z1), z2), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z1, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z2)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z2), z0, z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z2, bot[6])) PLUS#2(S(S(y0)), z1) -> c5(PLUS#2(S(y0), z1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x0)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x1), x2, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x0), x1, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x1, x2, x3), x4), x5, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x1, x2, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5), x6, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x0, x1, x2), x3), x4, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x0, x1, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4), x5, bot[0]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[7])) S tuples: COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, x2)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[6])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3), x4, x5) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3, bot[7])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0, x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x0, x1) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0)) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z2)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z2), z0, z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z2, bot[6])) PLUS#2(S(S(y0)), z1) -> c5(PLUS#2(S(y0), z1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x0)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x0), x1, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5), x6, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x0, x1, x2), x3), x4, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x0, x1, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4), x5, bot[0]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[7])) K tuples: COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(z1, z2, z3)), S(z4)) -> c3(COND_TAKE_L_N_XS(zipwith_l_f_xs_ys#1(z1, z2, z3, bot[0]), z4), ZIPWITH_L_F_XS_YS#1(z1, z2, z3, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, fibs_2(z1, z2, z3)), S(z4)) -> c2(COND_TAKE_L_N_XS(fibs_2#1(z1, z2, z3, bot[0]), z4)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x1)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x1), x2, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x1, x2, x3), x4), x5, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x1, x2, x3), x4, bot[7])) Defined Rule Symbols: zipwith_l_f_xs_ys#1_4, cond_zipwith_l_f_xs_ys_2, cond_zipwith_l_f_xs_ys_1_3, fibs_2#1_4, zipwith_l#3_2, plus#2_2 Defined Pair Symbols: COND_ZIPWITH_L_F_XS_YS_1_3, COND_TAKE_L_N_XS_2, COND_ZIPWITH_L_F_XS_YS_2, ZIPWITH_L_F_XS_YS#1_4, PLUS#2_2 Compound Symbols: c6_1, c3_2, c3_1, c8_2, c8_1, c12_2, c12_1, c2_1, c9_1, c11_1, c5_1, c10_1, c_1, c1_1, c4_1 ---------------------------------------- (107) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID)) Split RHS of tuples not part of any SCC ---------------------------------------- (108) Obligation: Complexity Dependency Tuples Problem Rules: zipwith_l_f_xs_ys#1(plus, fibs, z0, z1) -> cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0) zipwith_l_f_xs_ys#1(plus, fibs_2(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3) zipwith_l_f_xs_ys#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), zipwith_l_f_xs_ys(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), fibs_2(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys_1(ConsL(z0, z1), z2, z3) -> ConsL(plus#2(z2, z0), zipwith_l#3(z3, z1)) fibs_2#1(zipwith_l, plus, tail_l, z0) -> ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))) zipwith_l#3(z0, z1) -> zipwith_l_f_xs_ys(plus, z0, z1) plus#2(0, z0) -> z0 plus#2(S(z0), z1) -> S(plus#2(z0, z1)) Tuples: COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, x1)), S(x2)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs_2(x1, x2, x3), x4)), S(x5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x1, x2, x3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4)), S(x5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, x2)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[6])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3), x4, x5) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3, bot[7])) COND_TAKE_L_N_XS(ConsL(x0, fibs_2(zipwith_l, plus, tail_l)), S(x1)) -> c2(COND_TAKE_L_N_XS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x1)) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0, x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x0, x1) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0)) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z1)), S(z2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z1), z2), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z1, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z2)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z2), z0, z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z2, bot[6])) PLUS#2(S(S(y0)), z1) -> c5(PLUS#2(S(y0), z1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x0)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x1), x2, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x0), x1, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x1, x2, x3), x4), x5, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x1, x2, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5), x6, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x0, x1, x2), x3), x4, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x0, x1, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4), x5, bot[0]) -> c7(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4), x5, bot[0]) -> c7(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4, bot[7])) S tuples: COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, x2)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[6])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3), x4, x5) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3, bot[7])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0, x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x0, x1) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0)) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z2)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z2), z0, z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z2, bot[6])) PLUS#2(S(S(y0)), z1) -> c5(PLUS#2(S(y0), z1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x0)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x0), x1, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5), x6, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x0, x1, x2), x3), x4, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x0, x1, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4), x5, bot[0]) -> c7(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4), x5, bot[0]) -> c7(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4, bot[7])) K tuples: COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(z1, z2, z3)), S(z4)) -> c3(COND_TAKE_L_N_XS(zipwith_l_f_xs_ys#1(z1, z2, z3, bot[0]), z4), ZIPWITH_L_F_XS_YS#1(z1, z2, z3, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, fibs_2(z1, z2, z3)), S(z4)) -> c2(COND_TAKE_L_N_XS(fibs_2#1(z1, z2, z3, bot[0]), z4)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x1)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x1), x2, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x1, x2, x3), x4), x5, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x1, x2, x3), x4, bot[7])) Defined Rule Symbols: zipwith_l_f_xs_ys#1_4, cond_zipwith_l_f_xs_ys_2, cond_zipwith_l_f_xs_ys_1_3, fibs_2#1_4, zipwith_l#3_2, plus#2_2 Defined Pair Symbols: COND_ZIPWITH_L_F_XS_YS_1_3, COND_TAKE_L_N_XS_2, COND_ZIPWITH_L_F_XS_YS_2, ZIPWITH_L_F_XS_YS#1_4, PLUS#2_2 Compound Symbols: c6_1, c3_2, c3_1, c8_2, c8_1, c12_2, c12_1, c2_1, c9_1, c11_1, c5_1, c10_1, c_1, c1_1, c4_1, c7_1 ---------------------------------------- (109) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1))) Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S. ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4), x5, bot[0]) -> c7(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4), x5, bot[0]) -> c7(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4, bot[7])) We considered the (Usable) Rules:none And the Tuples: COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, x1)), S(x2)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs_2(x1, x2, x3), x4)), S(x5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x1, x2, x3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4)), S(x5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, x2)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[6])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3), x4, x5) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3, bot[7])) COND_TAKE_L_N_XS(ConsL(x0, fibs_2(zipwith_l, plus, tail_l)), S(x1)) -> c2(COND_TAKE_L_N_XS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x1)) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0, x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x0, x1) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0)) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z1)), S(z2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z1), z2), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z1, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z2)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z2), z0, z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z2, bot[6])) PLUS#2(S(S(y0)), z1) -> c5(PLUS#2(S(y0), z1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x0)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x1), x2, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x0), x1, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x1, x2, x3), x4), x5, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x1, x2, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5), x6, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x0, x1, x2), x3), x4, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x0, x1, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4), x5, bot[0]) -> c7(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4), x5, bot[0]) -> c7(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4, bot[7])) The order we found is given by the following interpretation: Polynomial interpretation : POL(0) = 0 POL(COND_TAKE_L_N_XS(x_1, x_2)) = [1] + x_2 POL(COND_ZIPWITH_L_F_XS_YS(x_1, x_2)) = 0 POL(COND_ZIPWITH_L_F_XS_YS_1(x_1, x_2, x_3)) = 0 POL(ConsL(x_1, x_2)) = 0 POL(PLUS#2(x_1, x_2)) = 0 POL(S(x_1)) = [1] + x_1 POL(ZIPWITH_L_F_XS_YS#1(x_1, x_2, x_3, x_4)) = x_1 + x_4 POL(bot[0]) = [1] POL(bot[6]) = 0 POL(bot[7]) = 0 POL(c(x_1)) = x_1 POL(c1(x_1)) = x_1 POL(c10(x_1)) = x_1 POL(c11(x_1)) = x_1 POL(c12(x_1)) = x_1 POL(c12(x_1, x_2)) = x_1 + x_2 POL(c2(x_1)) = x_1 POL(c3(x_1)) = x_1 POL(c3(x_1, x_2)) = x_1 + x_2 POL(c4(x_1)) = x_1 POL(c5(x_1)) = x_1 POL(c6(x_1)) = x_1 POL(c7(x_1)) = x_1 POL(c8(x_1)) = x_1 POL(c8(x_1, x_2)) = x_1 + x_2 POL(c9(x_1)) = x_1 POL(cond_zipwith_l_f_xs_ys(x_1, x_2)) = 0 POL(cond_zipwith_l_f_xs_ys_1(x_1, x_2, x_3)) = 0 POL(fibs) = 0 POL(fibs_2(x_1, x_2, x_3)) = 0 POL(fibs_2#1(x_1, x_2, x_3, x_4)) = x_1 + x_2 + x_3 POL(plus) = 0 POL(plus#2(x_1, x_2)) = [1] + x_1 + x_2 POL(tail_l) = 0 POL(zipwith_l) = 0 POL(zipwith_l#3(x_1, x_2)) = 0 POL(zipwith_l_f_xs_ys(x_1, x_2, x_3)) = 0 POL(zipwith_l_f_xs_ys#1(x_1, x_2, x_3, x_4)) = x_1 + x_2 + x_3 ---------------------------------------- (110) Obligation: Complexity Dependency Tuples Problem Rules: zipwith_l_f_xs_ys#1(plus, fibs, z0, z1) -> cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0) zipwith_l_f_xs_ys#1(plus, fibs_2(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3) zipwith_l_f_xs_ys#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), zipwith_l_f_xs_ys(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), fibs_2(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys_1(ConsL(z0, z1), z2, z3) -> ConsL(plus#2(z2, z0), zipwith_l#3(z3, z1)) fibs_2#1(zipwith_l, plus, tail_l, z0) -> ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))) zipwith_l#3(z0, z1) -> zipwith_l_f_xs_ys(plus, z0, z1) plus#2(0, z0) -> z0 plus#2(S(z0), z1) -> S(plus#2(z0, z1)) Tuples: COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, x1)), S(x2)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs_2(x1, x2, x3), x4)), S(x5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x1, x2, x3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4)), S(x5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, x2)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[6])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3), x4, x5) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3, bot[7])) COND_TAKE_L_N_XS(ConsL(x0, fibs_2(zipwith_l, plus, tail_l)), S(x1)) -> c2(COND_TAKE_L_N_XS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x1)) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0, x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x0, x1) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0)) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z1)), S(z2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z1), z2), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z1, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z2)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z2), z0, z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z2, bot[6])) PLUS#2(S(S(y0)), z1) -> c5(PLUS#2(S(y0), z1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x0)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x1), x2, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x0), x1, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x1, x2, x3), x4), x5, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x1, x2, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5), x6, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x0, x1, x2), x3), x4, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x0, x1, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4), x5, bot[0]) -> c7(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4), x5, bot[0]) -> c7(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4, bot[7])) S tuples: COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, x2)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[6])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3), x4, x5) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3, bot[7])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0, x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x0, x1) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0)) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z2)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z2), z0, z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z2, bot[6])) PLUS#2(S(S(y0)), z1) -> c5(PLUS#2(S(y0), z1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x0)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x0), x1, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5), x6, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x0, x1, x2), x3), x4, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x0, x1, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[7])) K tuples: COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(z1, z2, z3)), S(z4)) -> c3(COND_TAKE_L_N_XS(zipwith_l_f_xs_ys#1(z1, z2, z3, bot[0]), z4), ZIPWITH_L_F_XS_YS#1(z1, z2, z3, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, fibs_2(z1, z2, z3)), S(z4)) -> c2(COND_TAKE_L_N_XS(fibs_2#1(z1, z2, z3, bot[0]), z4)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x1)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x1), x2, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x1, x2, x3), x4), x5, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x1, x2, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4), x5, bot[0]) -> c7(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4), x5, bot[0]) -> c7(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4, bot[7])) Defined Rule Symbols: zipwith_l_f_xs_ys#1_4, cond_zipwith_l_f_xs_ys_2, cond_zipwith_l_f_xs_ys_1_3, fibs_2#1_4, zipwith_l#3_2, plus#2_2 Defined Pair Symbols: COND_ZIPWITH_L_F_XS_YS_1_3, COND_TAKE_L_N_XS_2, COND_ZIPWITH_L_F_XS_YS_2, ZIPWITH_L_F_XS_YS#1_4, PLUS#2_2 Compound Symbols: c6_1, c3_2, c3_1, c8_2, c8_1, c12_2, c12_1, c2_1, c9_1, c11_1, c5_1, c10_1, c_1, c1_1, c4_1, c7_1 ---------------------------------------- (111) CdtInstantiationProof (BOTH BOUNDS(ID, ID)) Use instantiation to replace ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x3, bot[7])) by ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4), x5, bot[0]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x2), x3, bot[7])) ---------------------------------------- (112) Obligation: Complexity Dependency Tuples Problem Rules: zipwith_l_f_xs_ys#1(plus, fibs, z0, z1) -> cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0) zipwith_l_f_xs_ys#1(plus, fibs_2(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3) zipwith_l_f_xs_ys#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), zipwith_l_f_xs_ys(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), fibs_2(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys_1(ConsL(z0, z1), z2, z3) -> ConsL(plus#2(z2, z0), zipwith_l#3(z3, z1)) fibs_2#1(zipwith_l, plus, tail_l, z0) -> ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))) zipwith_l#3(z0, z1) -> zipwith_l_f_xs_ys(plus, z0, z1) plus#2(0, z0) -> z0 plus#2(S(z0), z1) -> S(plus#2(z0, z1)) Tuples: COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, x1)), S(x2)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs_2(x1, x2, x3), x4)), S(x5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x1, x2, x3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4)), S(x5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, x2)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[6])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3), x4, x5) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3, bot[7])) COND_TAKE_L_N_XS(ConsL(x0, fibs_2(zipwith_l, plus, tail_l)), S(x1)) -> c2(COND_TAKE_L_N_XS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x1)) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0, x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x0, x1) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0)) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z1)), S(z2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z1), z2), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z1, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z2)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z2), z0, z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z2, bot[6])) PLUS#2(S(S(y0)), z1) -> c5(PLUS#2(S(y0), z1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x0)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x1), x2, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x0), x1, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x1, x2, x3), x4), x5, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x1, x2, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5), x6, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x0, x1, x2), x3), x4, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x0, x1, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4), x5, bot[0]) -> c7(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4), x5, bot[0]) -> c7(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4), x5, bot[0]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x2), x3, bot[7])) S tuples: COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, x2)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[6])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3), x4, x5) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3, bot[7])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0, x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x0, x1) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0)) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z2)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z2), z0, z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z2, bot[6])) PLUS#2(S(S(y0)), z1) -> c5(PLUS#2(S(y0), z1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x0)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x0), x1, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5), x6, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x0, x1, x2), x3), x4, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x0, x1, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4), x5, bot[0]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x2), x3, bot[7])) K tuples: COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(z1, z2, z3)), S(z4)) -> c3(COND_TAKE_L_N_XS(zipwith_l_f_xs_ys#1(z1, z2, z3, bot[0]), z4), ZIPWITH_L_F_XS_YS#1(z1, z2, z3, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, fibs_2(z1, z2, z3)), S(z4)) -> c2(COND_TAKE_L_N_XS(fibs_2#1(z1, z2, z3, bot[0]), z4)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x1)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x1), x2, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x1, x2, x3), x4), x5, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x1, x2, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4), x5, bot[0]) -> c7(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4), x5, bot[0]) -> c7(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4, bot[7])) Defined Rule Symbols: zipwith_l_f_xs_ys#1_4, cond_zipwith_l_f_xs_ys_2, cond_zipwith_l_f_xs_ys_1_3, fibs_2#1_4, zipwith_l#3_2, plus#2_2 Defined Pair Symbols: COND_ZIPWITH_L_F_XS_YS_1_3, COND_TAKE_L_N_XS_2, COND_ZIPWITH_L_F_XS_YS_2, ZIPWITH_L_F_XS_YS#1_4, PLUS#2_2 Compound Symbols: c6_1, c3_2, c3_1, c8_2, c8_1, c12_2, c12_1, c2_1, c9_1, c11_1, c5_1, c10_1, c_1, c1_1, c4_1, c7_1 ---------------------------------------- (113) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID)) Split RHS of tuples not part of any SCC ---------------------------------------- (114) Obligation: Complexity Dependency Tuples Problem Rules: zipwith_l_f_xs_ys#1(plus, fibs, z0, z1) -> cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0) zipwith_l_f_xs_ys#1(plus, fibs_2(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3) zipwith_l_f_xs_ys#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), zipwith_l_f_xs_ys(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), fibs_2(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys_1(ConsL(z0, z1), z2, z3) -> ConsL(plus#2(z2, z0), zipwith_l#3(z3, z1)) fibs_2#1(zipwith_l, plus, tail_l, z0) -> ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))) zipwith_l#3(z0, z1) -> zipwith_l_f_xs_ys(plus, z0, z1) plus#2(0, z0) -> z0 plus#2(S(z0), z1) -> S(plus#2(z0, z1)) Tuples: COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, x1)), S(x2)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs_2(x1, x2, x3), x4)), S(x5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x1, x2, x3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4)), S(x5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, x2)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[6])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3), x4, x5) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3, bot[7])) COND_TAKE_L_N_XS(ConsL(x0, fibs_2(zipwith_l, plus, tail_l)), S(x1)) -> c2(COND_TAKE_L_N_XS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x1)) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0, x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x0, x1) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0)) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z1)), S(z2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z1), z2), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z1, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z2)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z2), z0, z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z2, bot[6])) PLUS#2(S(S(y0)), z1) -> c5(PLUS#2(S(y0), z1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x0)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x1), x2, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x0), x1, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x1, x2, x3), x4), x5, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x1, x2, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5), x6, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x0, x1, x2), x3), x4, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x0, x1, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4), x5, bot[0]) -> c7(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4), x5, bot[0]) -> c7(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4), x5, bot[0]) -> c13(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4), x5, bot[0]) -> c13(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4, bot[7])) S tuples: COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, x2)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[6])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3), x4, x5) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3, bot[7])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0, x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x0, x1) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0)) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z2)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z2), z0, z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z2, bot[6])) PLUS#2(S(S(y0)), z1) -> c5(PLUS#2(S(y0), z1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x0)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x0), x1, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5), x6, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x0, x1, x2), x3), x4, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x0, x1, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4), x5, bot[0]) -> c13(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4), x5, bot[0]) -> c13(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4, bot[7])) K tuples: COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(z1, z2, z3)), S(z4)) -> c3(COND_TAKE_L_N_XS(zipwith_l_f_xs_ys#1(z1, z2, z3, bot[0]), z4), ZIPWITH_L_F_XS_YS#1(z1, z2, z3, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, fibs_2(z1, z2, z3)), S(z4)) -> c2(COND_TAKE_L_N_XS(fibs_2#1(z1, z2, z3, bot[0]), z4)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x1)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x1), x2, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x1, x2, x3), x4), x5, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x1, x2, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4), x5, bot[0]) -> c7(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4), x5, bot[0]) -> c7(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4, bot[7])) Defined Rule Symbols: zipwith_l_f_xs_ys#1_4, cond_zipwith_l_f_xs_ys_2, cond_zipwith_l_f_xs_ys_1_3, fibs_2#1_4, zipwith_l#3_2, plus#2_2 Defined Pair Symbols: COND_ZIPWITH_L_F_XS_YS_1_3, COND_TAKE_L_N_XS_2, COND_ZIPWITH_L_F_XS_YS_2, ZIPWITH_L_F_XS_YS#1_4, PLUS#2_2 Compound Symbols: c6_1, c3_2, c3_1, c8_2, c8_1, c12_2, c12_1, c2_1, c9_1, c11_1, c5_1, c10_1, c_1, c1_1, c4_1, c7_1, c13_1 ---------------------------------------- (115) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1))) Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S. ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4), x5, bot[0]) -> c13(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4), x5, bot[0]) -> c13(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4, bot[7])) We considered the (Usable) Rules:none And the Tuples: COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, x1)), S(x2)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs_2(x1, x2, x3), x4)), S(x5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x1, x2, x3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4)), S(x5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, x2)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[6])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3), x4, x5) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3, bot[7])) COND_TAKE_L_N_XS(ConsL(x0, fibs_2(zipwith_l, plus, tail_l)), S(x1)) -> c2(COND_TAKE_L_N_XS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x1)) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0, x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x0, x1) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0)) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z1)), S(z2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z1), z2), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z1, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z2)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z2), z0, z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z2, bot[6])) PLUS#2(S(S(y0)), z1) -> c5(PLUS#2(S(y0), z1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x0)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x1), x2, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x0), x1, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x1, x2, x3), x4), x5, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x1, x2, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5), x6, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x0, x1, x2), x3), x4, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x0, x1, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4), x5, bot[0]) -> c7(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4), x5, bot[0]) -> c7(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4), x5, bot[0]) -> c13(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4), x5, bot[0]) -> c13(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4, bot[7])) The order we found is given by the following interpretation: Polynomial interpretation : POL(0) = 0 POL(COND_TAKE_L_N_XS(x_1, x_2)) = [1] + x_2 POL(COND_ZIPWITH_L_F_XS_YS(x_1, x_2)) = 0 POL(COND_ZIPWITH_L_F_XS_YS_1(x_1, x_2, x_3)) = 0 POL(ConsL(x_1, x_2)) = 0 POL(PLUS#2(x_1, x_2)) = 0 POL(S(x_1)) = [1] + x_1 POL(ZIPWITH_L_F_XS_YS#1(x_1, x_2, x_3, x_4)) = x_1 + x_4 POL(bot[0]) = [1] POL(bot[6]) = 0 POL(bot[7]) = 0 POL(c(x_1)) = x_1 POL(c1(x_1)) = x_1 POL(c10(x_1)) = x_1 POL(c11(x_1)) = x_1 POL(c12(x_1)) = x_1 POL(c12(x_1, x_2)) = x_1 + x_2 POL(c13(x_1)) = x_1 POL(c2(x_1)) = x_1 POL(c3(x_1)) = x_1 POL(c3(x_1, x_2)) = x_1 + x_2 POL(c4(x_1)) = x_1 POL(c5(x_1)) = x_1 POL(c6(x_1)) = x_1 POL(c7(x_1)) = x_1 POL(c8(x_1)) = x_1 POL(c8(x_1, x_2)) = x_1 + x_2 POL(c9(x_1)) = x_1 POL(cond_zipwith_l_f_xs_ys(x_1, x_2)) = 0 POL(cond_zipwith_l_f_xs_ys_1(x_1, x_2, x_3)) = 0 POL(fibs) = 0 POL(fibs_2(x_1, x_2, x_3)) = 0 POL(fibs_2#1(x_1, x_2, x_3, x_4)) = x_1 + x_2 + x_3 POL(plus) = 0 POL(plus#2(x_1, x_2)) = [1] + x_1 + x_2 POL(tail_l) = 0 POL(zipwith_l) = 0 POL(zipwith_l#3(x_1, x_2)) = 0 POL(zipwith_l_f_xs_ys(x_1, x_2, x_3)) = 0 POL(zipwith_l_f_xs_ys#1(x_1, x_2, x_3, x_4)) = x_1 + x_2 + x_3 ---------------------------------------- (116) Obligation: Complexity Dependency Tuples Problem Rules: zipwith_l_f_xs_ys#1(plus, fibs, z0, z1) -> cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0) zipwith_l_f_xs_ys#1(plus, fibs_2(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3) zipwith_l_f_xs_ys#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), zipwith_l_f_xs_ys(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), fibs_2(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys_1(ConsL(z0, z1), z2, z3) -> ConsL(plus#2(z2, z0), zipwith_l#3(z3, z1)) fibs_2#1(zipwith_l, plus, tail_l, z0) -> ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))) zipwith_l#3(z0, z1) -> zipwith_l_f_xs_ys(plus, z0, z1) plus#2(0, z0) -> z0 plus#2(S(z0), z1) -> S(plus#2(z0, z1)) Tuples: COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, x1)), S(x2)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs_2(x1, x2, x3), x4)), S(x5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x1, x2, x3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4)), S(x5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, x2)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[6])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3), x4, x5) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3, bot[7])) COND_TAKE_L_N_XS(ConsL(x0, fibs_2(zipwith_l, plus, tail_l)), S(x1)) -> c2(COND_TAKE_L_N_XS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x1)) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0, x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x0, x1) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0)) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z1)), S(z2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z1), z2), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z1, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z2)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z2), z0, z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z2, bot[6])) PLUS#2(S(S(y0)), z1) -> c5(PLUS#2(S(y0), z1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x0)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x1), x2, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x0), x1, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x1, x2, x3), x4), x5, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x1, x2, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5), x6, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x0, x1, x2), x3), x4, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x0, x1, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4), x5, bot[0]) -> c7(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4), x5, bot[0]) -> c7(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4), x5, bot[0]) -> c13(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4), x5, bot[0]) -> c13(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4, bot[7])) S tuples: COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, x2)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[6])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3), x4, x5) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3, bot[7])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0, x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x0, x1) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0)) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z2)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z2), z0, z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z2, bot[6])) PLUS#2(S(S(y0)), z1) -> c5(PLUS#2(S(y0), z1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x0)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x0), x1, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5), x6, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x0, x1, x2), x3), x4, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x0, x1, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x2), x3, bot[7])) K tuples: COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(z1, z2, z3)), S(z4)) -> c3(COND_TAKE_L_N_XS(zipwith_l_f_xs_ys#1(z1, z2, z3, bot[0]), z4), ZIPWITH_L_F_XS_YS#1(z1, z2, z3, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, fibs_2(z1, z2, z3)), S(z4)) -> c2(COND_TAKE_L_N_XS(fibs_2#1(z1, z2, z3, bot[0]), z4)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x1)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x1), x2, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x1, x2, x3), x4), x5, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x1, x2, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4), x5, bot[0]) -> c7(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4), x5, bot[0]) -> c7(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4), x5, bot[0]) -> c13(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4), x5, bot[0]) -> c13(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4, bot[7])) Defined Rule Symbols: zipwith_l_f_xs_ys#1_4, cond_zipwith_l_f_xs_ys_2, cond_zipwith_l_f_xs_ys_1_3, fibs_2#1_4, zipwith_l#3_2, plus#2_2 Defined Pair Symbols: COND_ZIPWITH_L_F_XS_YS_1_3, COND_TAKE_L_N_XS_2, COND_ZIPWITH_L_F_XS_YS_2, ZIPWITH_L_F_XS_YS#1_4, PLUS#2_2 Compound Symbols: c6_1, c3_2, c3_1, c8_2, c8_1, c12_2, c12_1, c2_1, c9_1, c11_1, c5_1, c10_1, c_1, c1_1, c4_1, c7_1, c13_1 ---------------------------------------- (117) CdtInstantiationProof (BOTH BOUNDS(ID, ID)) Use instantiation to replace ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3), x4, x5) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x3, bot[7])) by ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4), x5, bot[0]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3, bot[7])) ---------------------------------------- (118) Obligation: Complexity Dependency Tuples Problem Rules: zipwith_l_f_xs_ys#1(plus, fibs, z0, z1) -> cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0) zipwith_l_f_xs_ys#1(plus, fibs_2(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3) zipwith_l_f_xs_ys#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), zipwith_l_f_xs_ys(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), fibs_2(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys_1(ConsL(z0, z1), z2, z3) -> ConsL(plus#2(z2, z0), zipwith_l#3(z3, z1)) fibs_2#1(zipwith_l, plus, tail_l, z0) -> ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))) zipwith_l#3(z0, z1) -> zipwith_l_f_xs_ys(plus, z0, z1) plus#2(0, z0) -> z0 plus#2(S(z0), z1) -> S(plus#2(z0, z1)) Tuples: COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, x1)), S(x2)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs_2(x1, x2, x3), x4)), S(x5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x1, x2, x3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4)), S(x5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, x2)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[6])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3), x4, x5) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3, bot[7])) COND_TAKE_L_N_XS(ConsL(x0, fibs_2(zipwith_l, plus, tail_l)), S(x1)) -> c2(COND_TAKE_L_N_XS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x1)) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0, x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x0, x1) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0)) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z1)), S(z2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z1), z2), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z1, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z2)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z2), z0, z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z2, bot[6])) PLUS#2(S(S(y0)), z1) -> c5(PLUS#2(S(y0), z1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x0)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x1), x2, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x0), x1, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x1, x2, x3), x4), x5, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x1, x2, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5), x6, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x0, x1, x2), x3), x4, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x0, x1, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4), x5, bot[0]) -> c7(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4), x5, bot[0]) -> c7(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4), x5, bot[0]) -> c13(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4), x5, bot[0]) -> c13(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4), x5, bot[0]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3, bot[7])) S tuples: COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, x2)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[6])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3), x4, x5) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3, bot[7])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0, x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x0, x1) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0)) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z2)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z2), z0, z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z2, bot[6])) PLUS#2(S(S(y0)), z1) -> c5(PLUS#2(S(y0), z1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x0)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x0), x1, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5), x6, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x0, x1, x2), x3), x4, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x0, x1, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4), x5, bot[0]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3, bot[7])) K tuples: COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(z1, z2, z3)), S(z4)) -> c3(COND_TAKE_L_N_XS(zipwith_l_f_xs_ys#1(z1, z2, z3, bot[0]), z4), ZIPWITH_L_F_XS_YS#1(z1, z2, z3, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, fibs_2(z1, z2, z3)), S(z4)) -> c2(COND_TAKE_L_N_XS(fibs_2#1(z1, z2, z3, bot[0]), z4)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x1)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x1), x2, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x1, x2, x3), x4), x5, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x1, x2, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4), x5, bot[0]) -> c7(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4), x5, bot[0]) -> c7(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4), x5, bot[0]) -> c13(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4), x5, bot[0]) -> c13(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4, bot[7])) Defined Rule Symbols: zipwith_l_f_xs_ys#1_4, cond_zipwith_l_f_xs_ys_2, cond_zipwith_l_f_xs_ys_1_3, fibs_2#1_4, zipwith_l#3_2, plus#2_2 Defined Pair Symbols: COND_ZIPWITH_L_F_XS_YS_1_3, COND_TAKE_L_N_XS_2, COND_ZIPWITH_L_F_XS_YS_2, ZIPWITH_L_F_XS_YS#1_4, PLUS#2_2 Compound Symbols: c6_1, c3_2, c3_1, c8_2, c8_1, c12_1, c2_1, c9_1, c11_1, c5_1, c10_1, c12_2, c_1, c1_1, c4_1, c7_1, c13_1 ---------------------------------------- (119) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID)) Split RHS of tuples not part of any SCC ---------------------------------------- (120) Obligation: Complexity Dependency Tuples Problem Rules: zipwith_l_f_xs_ys#1(plus, fibs, z0, z1) -> cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0) zipwith_l_f_xs_ys#1(plus, fibs_2(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3) zipwith_l_f_xs_ys#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), zipwith_l_f_xs_ys(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), fibs_2(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys_1(ConsL(z0, z1), z2, z3) -> ConsL(plus#2(z2, z0), zipwith_l#3(z3, z1)) fibs_2#1(zipwith_l, plus, tail_l, z0) -> ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))) zipwith_l#3(z0, z1) -> zipwith_l_f_xs_ys(plus, z0, z1) plus#2(0, z0) -> z0 plus#2(S(z0), z1) -> S(plus#2(z0, z1)) Tuples: COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, x1)), S(x2)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs_2(x1, x2, x3), x4)), S(x5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x1, x2, x3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4)), S(x5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, x2)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[6])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3), x4, x5) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3, bot[7])) COND_TAKE_L_N_XS(ConsL(x0, fibs_2(zipwith_l, plus, tail_l)), S(x1)) -> c2(COND_TAKE_L_N_XS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x1)) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0, x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x0, x1) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0)) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z1)), S(z2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z1), z2), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z1, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z2)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z2), z0, z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z2, bot[6])) PLUS#2(S(S(y0)), z1) -> c5(PLUS#2(S(y0), z1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x0)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x1), x2, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x0), x1, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x1, x2, x3), x4), x5, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x1, x2, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5), x6, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x0, x1, x2), x3), x4, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x0, x1, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4), x5, bot[0]) -> c7(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4), x5, bot[0]) -> c7(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4), x5, bot[0]) -> c13(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4), x5, bot[0]) -> c13(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4), x5, bot[0]) -> c14(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4), x5, bot[0]) -> c14(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4, bot[7])) S tuples: COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, x2)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[6])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3), x4, x5) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3, bot[7])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0, x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x0, x1) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0)) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z2)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z2), z0, z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z2, bot[6])) PLUS#2(S(S(y0)), z1) -> c5(PLUS#2(S(y0), z1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x0)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x0), x1, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5), x6, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x0, x1, x2), x3), x4, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x0, x1, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4), x5, bot[0]) -> c14(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4), x5, bot[0]) -> c14(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4, bot[7])) K tuples: COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(z1, z2, z3)), S(z4)) -> c3(COND_TAKE_L_N_XS(zipwith_l_f_xs_ys#1(z1, z2, z3, bot[0]), z4), ZIPWITH_L_F_XS_YS#1(z1, z2, z3, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, fibs_2(z1, z2, z3)), S(z4)) -> c2(COND_TAKE_L_N_XS(fibs_2#1(z1, z2, z3, bot[0]), z4)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x1)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x1), x2, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x1, x2, x3), x4), x5, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x1, x2, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4), x5, bot[0]) -> c7(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4), x5, bot[0]) -> c7(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4), x5, bot[0]) -> c13(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4), x5, bot[0]) -> c13(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4, bot[7])) Defined Rule Symbols: zipwith_l_f_xs_ys#1_4, cond_zipwith_l_f_xs_ys_2, cond_zipwith_l_f_xs_ys_1_3, fibs_2#1_4, zipwith_l#3_2, plus#2_2 Defined Pair Symbols: COND_ZIPWITH_L_F_XS_YS_1_3, COND_TAKE_L_N_XS_2, COND_ZIPWITH_L_F_XS_YS_2, ZIPWITH_L_F_XS_YS#1_4, PLUS#2_2 Compound Symbols: c6_1, c3_2, c3_1, c8_2, c8_1, c12_1, c2_1, c9_1, c11_1, c5_1, c10_1, c12_2, c_1, c1_1, c4_1, c7_1, c13_1, c14_1 ---------------------------------------- (121) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1))) Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S. ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4), x5, bot[0]) -> c14(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4), x5, bot[0]) -> c14(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4, bot[7])) We considered the (Usable) Rules:none And the Tuples: COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, x1)), S(x2)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs_2(x1, x2, x3), x4)), S(x5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x1, x2, x3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4)), S(x5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, x2)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[6])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3), x4, x5) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3, bot[7])) COND_TAKE_L_N_XS(ConsL(x0, fibs_2(zipwith_l, plus, tail_l)), S(x1)) -> c2(COND_TAKE_L_N_XS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x1)) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0, x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x0, x1) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0)) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z1)), S(z2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z1), z2), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z1, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z2)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z2), z0, z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z2, bot[6])) PLUS#2(S(S(y0)), z1) -> c5(PLUS#2(S(y0), z1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x0)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x1), x2, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x0), x1, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x1, x2, x3), x4), x5, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x1, x2, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5), x6, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x0, x1, x2), x3), x4, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x0, x1, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4), x5, bot[0]) -> c7(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4), x5, bot[0]) -> c7(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4), x5, bot[0]) -> c13(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4), x5, bot[0]) -> c13(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4), x5, bot[0]) -> c14(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4), x5, bot[0]) -> c14(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4, bot[7])) The order we found is given by the following interpretation: Polynomial interpretation : POL(0) = 0 POL(COND_TAKE_L_N_XS(x_1, x_2)) = x_2 POL(COND_ZIPWITH_L_F_XS_YS(x_1, x_2)) = 0 POL(COND_ZIPWITH_L_F_XS_YS_1(x_1, x_2, x_3)) = 0 POL(ConsL(x_1, x_2)) = 0 POL(PLUS#2(x_1, x_2)) = 0 POL(S(x_1)) = [1] + x_1 POL(ZIPWITH_L_F_XS_YS#1(x_1, x_2, x_3, x_4)) = x_1 + x_4 POL(bot[0]) = [1] POL(bot[6]) = 0 POL(bot[7]) = 0 POL(c(x_1)) = x_1 POL(c1(x_1)) = x_1 POL(c10(x_1)) = x_1 POL(c11(x_1)) = x_1 POL(c12(x_1)) = x_1 POL(c12(x_1, x_2)) = x_1 + x_2 POL(c13(x_1)) = x_1 POL(c14(x_1)) = x_1 POL(c2(x_1)) = x_1 POL(c3(x_1)) = x_1 POL(c3(x_1, x_2)) = x_1 + x_2 POL(c4(x_1)) = x_1 POL(c5(x_1)) = x_1 POL(c6(x_1)) = x_1 POL(c7(x_1)) = x_1 POL(c8(x_1)) = x_1 POL(c8(x_1, x_2)) = x_1 + x_2 POL(c9(x_1)) = x_1 POL(cond_zipwith_l_f_xs_ys(x_1, x_2)) = 0 POL(cond_zipwith_l_f_xs_ys_1(x_1, x_2, x_3)) = 0 POL(fibs) = 0 POL(fibs_2(x_1, x_2, x_3)) = 0 POL(fibs_2#1(x_1, x_2, x_3, x_4)) = x_1 + x_2 + x_3 POL(plus) = 0 POL(plus#2(x_1, x_2)) = [1] + x_1 + x_2 POL(tail_l) = 0 POL(zipwith_l) = 0 POL(zipwith_l#3(x_1, x_2)) = 0 POL(zipwith_l_f_xs_ys(x_1, x_2, x_3)) = 0 POL(zipwith_l_f_xs_ys#1(x_1, x_2, x_3, x_4)) = x_1 + x_2 + x_3 ---------------------------------------- (122) Obligation: Complexity Dependency Tuples Problem Rules: zipwith_l_f_xs_ys#1(plus, fibs, z0, z1) -> cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0) zipwith_l_f_xs_ys#1(plus, fibs_2(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3) zipwith_l_f_xs_ys#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), zipwith_l_f_xs_ys(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), fibs_2(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys_1(ConsL(z0, z1), z2, z3) -> ConsL(plus#2(z2, z0), zipwith_l#3(z3, z1)) fibs_2#1(zipwith_l, plus, tail_l, z0) -> ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))) zipwith_l#3(z0, z1) -> zipwith_l_f_xs_ys(plus, z0, z1) plus#2(0, z0) -> z0 plus#2(S(z0), z1) -> S(plus#2(z0, z1)) Tuples: COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, x1)), S(x2)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs_2(x1, x2, x3), x4)), S(x5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x1, x2, x3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4)), S(x5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, x2)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[6])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3), x4, x5) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3, bot[7])) COND_TAKE_L_N_XS(ConsL(x0, fibs_2(zipwith_l, plus, tail_l)), S(x1)) -> c2(COND_TAKE_L_N_XS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x1)) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0, x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x0, x1) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0)) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z1)), S(z2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z1), z2), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z1, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z2)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z2), z0, z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z2, bot[6])) PLUS#2(S(S(y0)), z1) -> c5(PLUS#2(S(y0), z1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x0)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x1), x2, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x0), x1, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x1, x2, x3), x4), x5, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x1, x2, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5), x6, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x0, x1, x2), x3), x4, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x0, x1, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4), x5, bot[0]) -> c7(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4), x5, bot[0]) -> c7(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4), x5, bot[0]) -> c13(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4), x5, bot[0]) -> c13(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4), x5, bot[0]) -> c14(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4), x5, bot[0]) -> c14(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4, bot[7])) S tuples: COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, x2)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[6])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3), x4, x5) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3, bot[7])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0, x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x0, x1) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0)) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z2)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z2), z0, z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z2, bot[6])) PLUS#2(S(S(y0)), z1) -> c5(PLUS#2(S(y0), z1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x0)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x0), x1, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5), x6, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x0, x1, x2), x3), x4, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x0, x1, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3, bot[7])) K tuples: COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(z1, z2, z3)), S(z4)) -> c3(COND_TAKE_L_N_XS(zipwith_l_f_xs_ys#1(z1, z2, z3, bot[0]), z4), ZIPWITH_L_F_XS_YS#1(z1, z2, z3, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, fibs_2(z1, z2, z3)), S(z4)) -> c2(COND_TAKE_L_N_XS(fibs_2#1(z1, z2, z3, bot[0]), z4)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x1)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x1), x2, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x1, x2, x3), x4), x5, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x1, x2, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4), x5, bot[0]) -> c7(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4), x5, bot[0]) -> c7(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4), x5, bot[0]) -> c13(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4), x5, bot[0]) -> c13(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4), x5, bot[0]) -> c14(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4), x5, bot[0]) -> c14(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4, bot[7])) Defined Rule Symbols: zipwith_l_f_xs_ys#1_4, cond_zipwith_l_f_xs_ys_2, cond_zipwith_l_f_xs_ys_1_3, fibs_2#1_4, zipwith_l#3_2, plus#2_2 Defined Pair Symbols: COND_ZIPWITH_L_F_XS_YS_1_3, COND_TAKE_L_N_XS_2, COND_ZIPWITH_L_F_XS_YS_2, ZIPWITH_L_F_XS_YS#1_4, PLUS#2_2 Compound Symbols: c6_1, c3_2, c3_1, c8_2, c8_1, c12_1, c2_1, c9_1, c11_1, c5_1, c10_1, c12_2, c_1, c1_1, c4_1, c7_1, c13_1, c14_1 ---------------------------------------- (123) CdtInstantiationProof (BOTH BOUNDS(ID, ID)) Use instantiation to replace ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3), x4, x5) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x0, x1, x2), x3, bot[7])) by ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4), x5, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5), x6, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2, bot[7])) ---------------------------------------- (124) Obligation: Complexity Dependency Tuples Problem Rules: zipwith_l_f_xs_ys#1(plus, fibs, z0, z1) -> cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0) zipwith_l_f_xs_ys#1(plus, fibs_2(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3) zipwith_l_f_xs_ys#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), zipwith_l_f_xs_ys(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), fibs_2(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys_1(ConsL(z0, z1), z2, z3) -> ConsL(plus#2(z2, z0), zipwith_l#3(z3, z1)) fibs_2#1(zipwith_l, plus, tail_l, z0) -> ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))) zipwith_l#3(z0, z1) -> zipwith_l_f_xs_ys(plus, z0, z1) plus#2(0, z0) -> z0 plus#2(S(z0), z1) -> S(plus#2(z0, z1)) Tuples: COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, x1)), S(x2)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs_2(x1, x2, x3), x4)), S(x5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x1, x2, x3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4)), S(x5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, x2)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[6])) COND_TAKE_L_N_XS(ConsL(x0, fibs_2(zipwith_l, plus, tail_l)), S(x1)) -> c2(COND_TAKE_L_N_XS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x1)) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0, x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x0, x1) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0)) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z1)), S(z2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z1), z2), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z1, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z2)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z2), z0, z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z2, bot[6])) PLUS#2(S(S(y0)), z1) -> c5(PLUS#2(S(y0), z1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x0)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x1), x2, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x0), x1, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x1, x2, x3), x4), x5, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x1, x2, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5), x6, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x0, x1, x2), x3), x4, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x0, x1, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4), x5, bot[0]) -> c7(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4), x5, bot[0]) -> c7(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4), x5, bot[0]) -> c13(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4), x5, bot[0]) -> c13(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4), x5, bot[0]) -> c14(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4), x5, bot[0]) -> c14(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4), x5, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5), x6, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2, bot[7])) S tuples: COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, x2)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0, x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x0, x1) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0)) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z2)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z2), z0, z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z2, bot[6])) PLUS#2(S(S(y0)), z1) -> c5(PLUS#2(S(y0), z1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x0)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x0), x1, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5), x6, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x0, x1, x2), x3), x4, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x0, x1, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4), x5, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5), x6, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2, bot[7])) K tuples: COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(z1, z2, z3)), S(z4)) -> c3(COND_TAKE_L_N_XS(zipwith_l_f_xs_ys#1(z1, z2, z3, bot[0]), z4), ZIPWITH_L_F_XS_YS#1(z1, z2, z3, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, fibs_2(z1, z2, z3)), S(z4)) -> c2(COND_TAKE_L_N_XS(fibs_2#1(z1, z2, z3, bot[0]), z4)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x1)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x1), x2, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x1, x2, x3), x4), x5, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x1, x2, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4), x5, bot[0]) -> c7(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4), x5, bot[0]) -> c7(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4), x5, bot[0]) -> c13(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4), x5, bot[0]) -> c13(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4), x5, bot[0]) -> c14(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4), x5, bot[0]) -> c14(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4, bot[7])) Defined Rule Symbols: zipwith_l_f_xs_ys#1_4, cond_zipwith_l_f_xs_ys_2, cond_zipwith_l_f_xs_ys_1_3, fibs_2#1_4, zipwith_l#3_2, plus#2_2 Defined Pair Symbols: COND_ZIPWITH_L_F_XS_YS_1_3, COND_TAKE_L_N_XS_2, COND_ZIPWITH_L_F_XS_YS_2, ZIPWITH_L_F_XS_YS#1_4, PLUS#2_2 Compound Symbols: c6_1, c3_2, c3_1, c8_2, c8_1, c2_1, c9_1, c11_1, c5_1, c10_1, c12_2, c_1, c1_1, c12_1, c4_1, c7_1, c13_1, c14_1 ---------------------------------------- (125) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1))) Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S. ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4), x5, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4, bot[7])) We considered the (Usable) Rules:none And the Tuples: COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, x1)), S(x2)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs_2(x1, x2, x3), x4)), S(x5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x1, x2, x3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4)), S(x5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, x2)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[6])) COND_TAKE_L_N_XS(ConsL(x0, fibs_2(zipwith_l, plus, tail_l)), S(x1)) -> c2(COND_TAKE_L_N_XS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x1)) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0, x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x0, x1) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0)) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z1)), S(z2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z1), z2), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z1, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z2)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z2), z0, z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z2, bot[6])) PLUS#2(S(S(y0)), z1) -> c5(PLUS#2(S(y0), z1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x0)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x1), x2, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x0), x1, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x1, x2, x3), x4), x5, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x1, x2, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5), x6, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x0, x1, x2), x3), x4, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x0, x1, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4), x5, bot[0]) -> c7(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4), x5, bot[0]) -> c7(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4), x5, bot[0]) -> c13(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4), x5, bot[0]) -> c13(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4), x5, bot[0]) -> c14(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4), x5, bot[0]) -> c14(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4), x5, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5), x6, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2, bot[7])) The order we found is given by the following interpretation: Polynomial interpretation : POL(0) = 0 POL(COND_TAKE_L_N_XS(x_1, x_2)) = x_2 POL(COND_ZIPWITH_L_F_XS_YS(x_1, x_2)) = 0 POL(COND_ZIPWITH_L_F_XS_YS_1(x_1, x_2, x_3)) = 0 POL(ConsL(x_1, x_2)) = 0 POL(PLUS#2(x_1, x_2)) = 0 POL(S(x_1)) = [1] + x_1 POL(ZIPWITH_L_F_XS_YS#1(x_1, x_2, x_3, x_4)) = x_1 + x_4 POL(bot[0]) = [1] POL(bot[6]) = 0 POL(bot[7]) = 0 POL(c(x_1)) = x_1 POL(c1(x_1)) = x_1 POL(c10(x_1)) = x_1 POL(c11(x_1)) = x_1 POL(c12(x_1)) = x_1 POL(c12(x_1, x_2)) = x_1 + x_2 POL(c13(x_1)) = x_1 POL(c14(x_1)) = x_1 POL(c2(x_1)) = x_1 POL(c3(x_1)) = x_1 POL(c3(x_1, x_2)) = x_1 + x_2 POL(c4(x_1)) = x_1 POL(c5(x_1)) = x_1 POL(c6(x_1)) = x_1 POL(c7(x_1)) = x_1 POL(c8(x_1)) = x_1 POL(c8(x_1, x_2)) = x_1 + x_2 POL(c9(x_1)) = x_1 POL(cond_zipwith_l_f_xs_ys(x_1, x_2)) = 0 POL(cond_zipwith_l_f_xs_ys_1(x_1, x_2, x_3)) = 0 POL(fibs) = 0 POL(fibs_2(x_1, x_2, x_3)) = 0 POL(fibs_2#1(x_1, x_2, x_3, x_4)) = x_1 + x_2 + x_3 POL(plus) = 0 POL(plus#2(x_1, x_2)) = [1] + x_1 + x_2 POL(tail_l) = 0 POL(zipwith_l) = 0 POL(zipwith_l#3(x_1, x_2)) = 0 POL(zipwith_l_f_xs_ys(x_1, x_2, x_3)) = 0 POL(zipwith_l_f_xs_ys#1(x_1, x_2, x_3, x_4)) = x_1 + x_2 + x_3 ---------------------------------------- (126) Obligation: Complexity Dependency Tuples Problem Rules: zipwith_l_f_xs_ys#1(plus, fibs, z0, z1) -> cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0) zipwith_l_f_xs_ys#1(plus, fibs_2(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3) zipwith_l_f_xs_ys#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), zipwith_l_f_xs_ys(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), fibs_2(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys_1(ConsL(z0, z1), z2, z3) -> ConsL(plus#2(z2, z0), zipwith_l#3(z3, z1)) fibs_2#1(zipwith_l, plus, tail_l, z0) -> ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))) zipwith_l#3(z0, z1) -> zipwith_l_f_xs_ys(plus, z0, z1) plus#2(0, z0) -> z0 plus#2(S(z0), z1) -> S(plus#2(z0, z1)) Tuples: COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, x1)), S(x2)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs_2(x1, x2, x3), x4)), S(x5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x1, x2, x3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4)), S(x5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, x2)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[6])) COND_TAKE_L_N_XS(ConsL(x0, fibs_2(zipwith_l, plus, tail_l)), S(x1)) -> c2(COND_TAKE_L_N_XS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x1)) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0, x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x0, x1) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0)) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z1)), S(z2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z1), z2), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z1, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z2)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z2), z0, z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z2, bot[6])) PLUS#2(S(S(y0)), z1) -> c5(PLUS#2(S(y0), z1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x0)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x1), x2, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x0), x1, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x1, x2, x3), x4), x5, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x1, x2, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5), x6, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x0, x1, x2), x3), x4, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x0, x1, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4), x5, bot[0]) -> c7(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4), x5, bot[0]) -> c7(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4), x5, bot[0]) -> c13(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4), x5, bot[0]) -> c13(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4), x5, bot[0]) -> c14(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4), x5, bot[0]) -> c14(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4), x5, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5), x6, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2, bot[7])) S tuples: COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, x2)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0, x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x0, x1) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0)) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z2)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z2), z0, z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z2, bot[6])) PLUS#2(S(S(y0)), z1) -> c5(PLUS#2(S(y0), z1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x0)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x0), x1, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5), x6, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x0, x1, x2), x3), x4, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x0, x1, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5), x6, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2, bot[7])) K tuples: COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(z1, z2, z3)), S(z4)) -> c3(COND_TAKE_L_N_XS(zipwith_l_f_xs_ys#1(z1, z2, z3, bot[0]), z4), ZIPWITH_L_F_XS_YS#1(z1, z2, z3, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, fibs_2(z1, z2, z3)), S(z4)) -> c2(COND_TAKE_L_N_XS(fibs_2#1(z1, z2, z3, bot[0]), z4)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x1)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x1), x2, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x1, x2, x3), x4), x5, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x1, x2, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4), x5, bot[0]) -> c7(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4), x5, bot[0]) -> c7(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4), x5, bot[0]) -> c13(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4), x5, bot[0]) -> c13(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4), x5, bot[0]) -> c14(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4), x5, bot[0]) -> c14(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4), x5, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4, bot[7])) Defined Rule Symbols: zipwith_l_f_xs_ys#1_4, cond_zipwith_l_f_xs_ys_2, cond_zipwith_l_f_xs_ys_1_3, fibs_2#1_4, zipwith_l#3_2, plus#2_2 Defined Pair Symbols: COND_ZIPWITH_L_F_XS_YS_1_3, COND_TAKE_L_N_XS_2, COND_ZIPWITH_L_F_XS_YS_2, ZIPWITH_L_F_XS_YS#1_4, PLUS#2_2 Compound Symbols: c6_1, c3_2, c3_1, c8_2, c8_1, c2_1, c9_1, c11_1, c5_1, c10_1, c12_2, c_1, c1_1, c12_1, c4_1, c7_1, c13_1, c14_1 ---------------------------------------- (127) CdtInstantiationProof (BOTH BOUNDS(ID, ID)) Use instantiation to replace ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x0, x1) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0)) by ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[0]) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x4)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x5, bot[6]) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x5)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x0, bot[7]) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0)) ---------------------------------------- (128) Obligation: Complexity Dependency Tuples Problem Rules: zipwith_l_f_xs_ys#1(plus, fibs, z0, z1) -> cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0) zipwith_l_f_xs_ys#1(plus, fibs_2(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3) zipwith_l_f_xs_ys#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), zipwith_l_f_xs_ys(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), fibs_2(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys_1(ConsL(z0, z1), z2, z3) -> ConsL(plus#2(z2, z0), zipwith_l#3(z3, z1)) fibs_2#1(zipwith_l, plus, tail_l, z0) -> ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))) zipwith_l#3(z0, z1) -> zipwith_l_f_xs_ys(plus, z0, z1) plus#2(0, z0) -> z0 plus#2(S(z0), z1) -> S(plus#2(z0, z1)) Tuples: COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, x1)), S(x2)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs_2(x1, x2, x3), x4)), S(x5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x1, x2, x3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4)), S(x5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, x2)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[6])) COND_TAKE_L_N_XS(ConsL(x0, fibs_2(zipwith_l, plus, tail_l)), S(x1)) -> c2(COND_TAKE_L_N_XS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x1)) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0, x1)) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z1)), S(z2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z1), z2), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z1, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z2)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z2), z0, z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z2, bot[6])) PLUS#2(S(S(y0)), z1) -> c5(PLUS#2(S(y0), z1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x0)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x1), x2, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x0), x1, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x1, x2, x3), x4), x5, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x1, x2, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5), x6, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x0, x1, x2), x3), x4, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x0, x1, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4), x5, bot[0]) -> c7(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4), x5, bot[0]) -> c7(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4), x5, bot[0]) -> c13(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4), x5, bot[0]) -> c13(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4), x5, bot[0]) -> c14(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4), x5, bot[0]) -> c14(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4), x5, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5), x6, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[0]) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x4)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x5, bot[6]) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x5)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x0, bot[7]) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0)) S tuples: COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, x2)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0, x1)) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z2)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z2), z0, z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z2, bot[6])) PLUS#2(S(S(y0)), z1) -> c5(PLUS#2(S(y0), z1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x0)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x0), x1, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5), x6, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x0, x1, x2), x3), x4, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x0, x1, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5), x6, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[0]) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x4)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x5, bot[6]) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x5)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x0, bot[7]) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0)) K tuples: COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(z1, z2, z3)), S(z4)) -> c3(COND_TAKE_L_N_XS(zipwith_l_f_xs_ys#1(z1, z2, z3, bot[0]), z4), ZIPWITH_L_F_XS_YS#1(z1, z2, z3, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, fibs_2(z1, z2, z3)), S(z4)) -> c2(COND_TAKE_L_N_XS(fibs_2#1(z1, z2, z3, bot[0]), z4)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x1)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x1), x2, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x1, x2, x3), x4), x5, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x1, x2, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4), x5, bot[0]) -> c7(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4), x5, bot[0]) -> c7(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4), x5, bot[0]) -> c13(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4), x5, bot[0]) -> c13(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4), x5, bot[0]) -> c14(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4), x5, bot[0]) -> c14(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4), x5, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4, bot[7])) Defined Rule Symbols: zipwith_l_f_xs_ys#1_4, cond_zipwith_l_f_xs_ys_2, cond_zipwith_l_f_xs_ys_1_3, fibs_2#1_4, zipwith_l#3_2, plus#2_2 Defined Pair Symbols: COND_ZIPWITH_L_F_XS_YS_1_3, COND_TAKE_L_N_XS_2, COND_ZIPWITH_L_F_XS_YS_2, PLUS#2_2, ZIPWITH_L_F_XS_YS#1_4 Compound Symbols: c6_1, c3_2, c3_1, c8_2, c8_1, c2_1, c9_1, c5_1, c10_1, c12_2, c_1, c1_1, c12_1, c4_1, c7_1, c13_1, c14_1, c11_1 ---------------------------------------- (129) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1))) Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S. ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[0]) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x4)) We considered the (Usable) Rules:none And the Tuples: COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, x1)), S(x2)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs_2(x1, x2, x3), x4)), S(x5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x1, x2, x3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4)), S(x5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, x2)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[6])) COND_TAKE_L_N_XS(ConsL(x0, fibs_2(zipwith_l, plus, tail_l)), S(x1)) -> c2(COND_TAKE_L_N_XS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x1)) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0, x1)) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z1)), S(z2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z1), z2), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z1, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z2)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z2), z0, z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z2, bot[6])) PLUS#2(S(S(y0)), z1) -> c5(PLUS#2(S(y0), z1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x0)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x1), x2, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x0), x1, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x1, x2, x3), x4), x5, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x1, x2, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5), x6, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x0, x1, x2), x3), x4, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x0, x1, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4), x5, bot[0]) -> c7(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4), x5, bot[0]) -> c7(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4), x5, bot[0]) -> c13(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4), x5, bot[0]) -> c13(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4), x5, bot[0]) -> c14(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4), x5, bot[0]) -> c14(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4), x5, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5), x6, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[0]) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x4)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x5, bot[6]) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x5)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x0, bot[7]) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0)) The order we found is given by the following interpretation: Polynomial interpretation : POL(0) = 0 POL(COND_TAKE_L_N_XS(x_1, x_2)) = [1] + x_2 POL(COND_ZIPWITH_L_F_XS_YS(x_1, x_2)) = 0 POL(COND_ZIPWITH_L_F_XS_YS_1(x_1, x_2, x_3)) = 0 POL(ConsL(x_1, x_2)) = 0 POL(PLUS#2(x_1, x_2)) = 0 POL(S(x_1)) = [1] + x_1 POL(ZIPWITH_L_F_XS_YS#1(x_1, x_2, x_3, x_4)) = x_1 + x_4 POL(bot[0]) = [1] POL(bot[6]) = 0 POL(bot[7]) = 0 POL(c(x_1)) = x_1 POL(c1(x_1)) = x_1 POL(c10(x_1)) = x_1 POL(c11(x_1)) = x_1 POL(c12(x_1)) = x_1 POL(c12(x_1, x_2)) = x_1 + x_2 POL(c13(x_1)) = x_1 POL(c14(x_1)) = x_1 POL(c2(x_1)) = x_1 POL(c3(x_1)) = x_1 POL(c3(x_1, x_2)) = x_1 + x_2 POL(c4(x_1)) = x_1 POL(c5(x_1)) = x_1 POL(c6(x_1)) = x_1 POL(c7(x_1)) = x_1 POL(c8(x_1)) = x_1 POL(c8(x_1, x_2)) = x_1 + x_2 POL(c9(x_1)) = x_1 POL(cond_zipwith_l_f_xs_ys(x_1, x_2)) = 0 POL(cond_zipwith_l_f_xs_ys_1(x_1, x_2, x_3)) = 0 POL(fibs) = 0 POL(fibs_2(x_1, x_2, x_3)) = 0 POL(fibs_2#1(x_1, x_2, x_3, x_4)) = x_1 + x_2 + x_3 POL(plus) = 0 POL(plus#2(x_1, x_2)) = [1] + x_1 + x_2 POL(tail_l) = 0 POL(zipwith_l) = 0 POL(zipwith_l#3(x_1, x_2)) = 0 POL(zipwith_l_f_xs_ys(x_1, x_2, x_3)) = 0 POL(zipwith_l_f_xs_ys#1(x_1, x_2, x_3, x_4)) = x_1 + x_2 + x_3 ---------------------------------------- (130) Obligation: Complexity Dependency Tuples Problem Rules: zipwith_l_f_xs_ys#1(plus, fibs, z0, z1) -> cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0) zipwith_l_f_xs_ys#1(plus, fibs_2(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3) zipwith_l_f_xs_ys#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), zipwith_l_f_xs_ys(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), fibs_2(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys_1(ConsL(z0, z1), z2, z3) -> ConsL(plus#2(z2, z0), zipwith_l#3(z3, z1)) fibs_2#1(zipwith_l, plus, tail_l, z0) -> ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))) zipwith_l#3(z0, z1) -> zipwith_l_f_xs_ys(plus, z0, z1) plus#2(0, z0) -> z0 plus#2(S(z0), z1) -> S(plus#2(z0, z1)) Tuples: COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, x1)), S(x2)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs_2(x1, x2, x3), x4)), S(x5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x1, x2, x3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4)), S(x5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, x2)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[6])) COND_TAKE_L_N_XS(ConsL(x0, fibs_2(zipwith_l, plus, tail_l)), S(x1)) -> c2(COND_TAKE_L_N_XS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x1)) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0, x1)) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z1)), S(z2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z1), z2), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z1, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z2)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z2), z0, z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z2, bot[6])) PLUS#2(S(S(y0)), z1) -> c5(PLUS#2(S(y0), z1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x0)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x1), x2, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x0), x1, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x1, x2, x3), x4), x5, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x1, x2, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5), x6, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x0, x1, x2), x3), x4, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x0, x1, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4), x5, bot[0]) -> c7(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4), x5, bot[0]) -> c7(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4), x5, bot[0]) -> c13(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4), x5, bot[0]) -> c13(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4), x5, bot[0]) -> c14(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4), x5, bot[0]) -> c14(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4), x5, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5), x6, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[0]) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x4)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x5, bot[6]) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x5)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x0, bot[7]) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0)) S tuples: COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, x2)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0, x1)) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z2)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z2), z0, z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z2, bot[6])) PLUS#2(S(S(y0)), z1) -> c5(PLUS#2(S(y0), z1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x0)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x0), x1, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5), x6, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x0, x1, x2), x3), x4, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x0, x1, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5), x6, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x5, bot[6]) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x5)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x0, bot[7]) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0)) K tuples: COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(z1, z2, z3)), S(z4)) -> c3(COND_TAKE_L_N_XS(zipwith_l_f_xs_ys#1(z1, z2, z3, bot[0]), z4), ZIPWITH_L_F_XS_YS#1(z1, z2, z3, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, fibs_2(z1, z2, z3)), S(z4)) -> c2(COND_TAKE_L_N_XS(fibs_2#1(z1, z2, z3, bot[0]), z4)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x1)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x1), x2, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x1, x2, x3), x4), x5, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x1, x2, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4), x5, bot[0]) -> c7(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4), x5, bot[0]) -> c7(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4), x5, bot[0]) -> c13(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4), x5, bot[0]) -> c13(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4), x5, bot[0]) -> c14(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4), x5, bot[0]) -> c14(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4), x5, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[0]) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x4)) Defined Rule Symbols: zipwith_l_f_xs_ys#1_4, cond_zipwith_l_f_xs_ys_2, cond_zipwith_l_f_xs_ys_1_3, fibs_2#1_4, zipwith_l#3_2, plus#2_2 Defined Pair Symbols: COND_ZIPWITH_L_F_XS_YS_1_3, COND_TAKE_L_N_XS_2, COND_ZIPWITH_L_F_XS_YS_2, PLUS#2_2, ZIPWITH_L_F_XS_YS#1_4 Compound Symbols: c6_1, c3_2, c3_1, c8_2, c8_1, c2_1, c9_1, c5_1, c10_1, c12_2, c_1, c1_1, c12_1, c4_1, c7_1, c13_1, c14_1, c11_1 ---------------------------------------- (131) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) by COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), S(S(y0)), z3) -> c6(PLUS#2(S(S(y0)), z0)) ---------------------------------------- (132) Obligation: Complexity Dependency Tuples Problem Rules: zipwith_l_f_xs_ys#1(plus, fibs, z0, z1) -> cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0) zipwith_l_f_xs_ys#1(plus, fibs_2(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3) zipwith_l_f_xs_ys#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), zipwith_l_f_xs_ys(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), fibs_2(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys_1(ConsL(z0, z1), z2, z3) -> ConsL(plus#2(z2, z0), zipwith_l#3(z3, z1)) fibs_2#1(zipwith_l, plus, tail_l, z0) -> ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))) zipwith_l#3(z0, z1) -> zipwith_l_f_xs_ys(plus, z0, z1) plus#2(0, z0) -> z0 plus#2(S(z0), z1) -> S(plus#2(z0, z1)) Tuples: COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, x1)), S(x2)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs_2(x1, x2, x3), x4)), S(x5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x1, x2, x3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4)), S(x5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, x2)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[6])) COND_TAKE_L_N_XS(ConsL(x0, fibs_2(zipwith_l, plus, tail_l)), S(x1)) -> c2(COND_TAKE_L_N_XS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x1)) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0, x1)) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z1)), S(z2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z1), z2), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z1, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z2)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z2), z0, z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z2, bot[6])) PLUS#2(S(S(y0)), z1) -> c5(PLUS#2(S(y0), z1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x0)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x1), x2, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x0), x1, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x1, x2, x3), x4), x5, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x1, x2, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5), x6, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x0, x1, x2), x3), x4, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x0, x1, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4), x5, bot[0]) -> c7(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4), x5, bot[0]) -> c7(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4), x5, bot[0]) -> c13(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4), x5, bot[0]) -> c13(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4), x5, bot[0]) -> c14(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4), x5, bot[0]) -> c14(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4), x5, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5), x6, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[0]) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x4)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x5, bot[6]) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x5)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x0, bot[7]) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0)) COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), S(S(y0)), z3) -> c6(PLUS#2(S(S(y0)), z0)) S tuples: COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, x2)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0, x1)) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z2)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z2), z0, z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z2, bot[6])) PLUS#2(S(S(y0)), z1) -> c5(PLUS#2(S(y0), z1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x0)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x0), x1, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5), x6, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x0, x1, x2), x3), x4, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x0, x1, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5), x6, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x5, bot[6]) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x5)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x0, bot[7]) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0)) COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), S(S(y0)), z3) -> c6(PLUS#2(S(S(y0)), z0)) K tuples: COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(z1, z2, z3)), S(z4)) -> c3(COND_TAKE_L_N_XS(zipwith_l_f_xs_ys#1(z1, z2, z3, bot[0]), z4), ZIPWITH_L_F_XS_YS#1(z1, z2, z3, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, fibs_2(z1, z2, z3)), S(z4)) -> c2(COND_TAKE_L_N_XS(fibs_2#1(z1, z2, z3, bot[0]), z4)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x1)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x1), x2, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x1, x2, x3), x4), x5, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x1, x2, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4), x5, bot[0]) -> c7(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4), x5, bot[0]) -> c7(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4), x5, bot[0]) -> c13(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4), x5, bot[0]) -> c13(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4), x5, bot[0]) -> c14(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4), x5, bot[0]) -> c14(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4), x5, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[0]) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x4)) Defined Rule Symbols: zipwith_l_f_xs_ys#1_4, cond_zipwith_l_f_xs_ys_2, cond_zipwith_l_f_xs_ys_1_3, fibs_2#1_4, zipwith_l#3_2, plus#2_2 Defined Pair Symbols: COND_TAKE_L_N_XS_2, COND_ZIPWITH_L_F_XS_YS_2, PLUS#2_2, ZIPWITH_L_F_XS_YS#1_4, COND_ZIPWITH_L_F_XS_YS_1_3 Compound Symbols: c3_2, c3_1, c8_2, c8_1, c2_1, c9_1, c5_1, c10_1, c12_2, c_1, c1_1, c12_1, c4_1, c7_1, c13_1, c14_1, c11_1, c6_1 ---------------------------------------- (133) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs_2(x1, x2, x3), x4)), S(x5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x1, x2, x3), x4, bot[0])) by COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z4, bot[0])) ---------------------------------------- (134) Obligation: Complexity Dependency Tuples Problem Rules: zipwith_l_f_xs_ys#1(plus, fibs, z0, z1) -> cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0) zipwith_l_f_xs_ys#1(plus, fibs_2(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3) zipwith_l_f_xs_ys#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), zipwith_l_f_xs_ys(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), fibs_2(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys_1(ConsL(z0, z1), z2, z3) -> ConsL(plus#2(z2, z0), zipwith_l#3(z3, z1)) fibs_2#1(zipwith_l, plus, tail_l, z0) -> ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))) zipwith_l#3(z0, z1) -> zipwith_l_f_xs_ys(plus, z0, z1) plus#2(0, z0) -> z0 plus#2(S(z0), z1) -> S(plus#2(z0, z1)) Tuples: COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, x1)), S(x2)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4)), S(x5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, x2)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[6])) COND_TAKE_L_N_XS(ConsL(x0, fibs_2(zipwith_l, plus, tail_l)), S(x1)) -> c2(COND_TAKE_L_N_XS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x1)) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0, x1)) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z1)), S(z2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z1), z2), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z1, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z2)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z2), z0, z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z2, bot[6])) PLUS#2(S(S(y0)), z1) -> c5(PLUS#2(S(y0), z1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x0)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x1), x2, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x0), x1, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x1, x2, x3), x4), x5, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x1, x2, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5), x6, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x0, x1, x2), x3), x4, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x0, x1, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4), x5, bot[0]) -> c7(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4), x5, bot[0]) -> c7(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4), x5, bot[0]) -> c13(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4), x5, bot[0]) -> c13(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4), x5, bot[0]) -> c14(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4), x5, bot[0]) -> c14(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4), x5, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5), x6, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[0]) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x4)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x5, bot[6]) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x5)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x0, bot[7]) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0)) COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), S(S(y0)), z3) -> c6(PLUS#2(S(S(y0)), z0)) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z4, bot[0])) S tuples: COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, x2)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0, x1)) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z2)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z2), z0, z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z2, bot[6])) PLUS#2(S(S(y0)), z1) -> c5(PLUS#2(S(y0), z1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x0)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x0), x1, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5), x6, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x0, x1, x2), x3), x4, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x0, x1, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5), x6, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x5, bot[6]) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x5)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x0, bot[7]) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0)) COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), S(S(y0)), z3) -> c6(PLUS#2(S(S(y0)), z0)) K tuples: COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(z1, z2, z3)), S(z4)) -> c3(COND_TAKE_L_N_XS(zipwith_l_f_xs_ys#1(z1, z2, z3, bot[0]), z4), ZIPWITH_L_F_XS_YS#1(z1, z2, z3, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, fibs_2(z1, z2, z3)), S(z4)) -> c2(COND_TAKE_L_N_XS(fibs_2#1(z1, z2, z3, bot[0]), z4)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x1)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x1), x2, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x1, x2, x3), x4), x5, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x1, x2, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4), x5, bot[0]) -> c7(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4), x5, bot[0]) -> c7(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4), x5, bot[0]) -> c13(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4), x5, bot[0]) -> c13(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4), x5, bot[0]) -> c14(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4), x5, bot[0]) -> c14(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4), x5, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[0]) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x4)) Defined Rule Symbols: zipwith_l_f_xs_ys#1_4, cond_zipwith_l_f_xs_ys_2, cond_zipwith_l_f_xs_ys_1_3, fibs_2#1_4, zipwith_l#3_2, plus#2_2 Defined Pair Symbols: COND_TAKE_L_N_XS_2, COND_ZIPWITH_L_F_XS_YS_2, PLUS#2_2, ZIPWITH_L_F_XS_YS#1_4, COND_ZIPWITH_L_F_XS_YS_1_3 Compound Symbols: c3_2, c3_1, c8_2, c8_1, c2_1, c9_1, c5_1, c10_1, c12_2, c_1, c1_1, c12_1, c4_1, c7_1, c13_1, c14_1, c11_1, c6_1 ---------------------------------------- (135) CdtRewritingProof (BOTH BOUNDS(ID, ID)) Used rewriting to replace ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x5, bot[7])) by ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z0), z1, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z0), z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z0, bot[7])) ---------------------------------------- (136) Obligation: Complexity Dependency Tuples Problem Rules: zipwith_l_f_xs_ys#1(plus, fibs, z0, z1) -> cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0) zipwith_l_f_xs_ys#1(plus, fibs_2(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3) zipwith_l_f_xs_ys#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), zipwith_l_f_xs_ys(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), fibs_2(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys_1(ConsL(z0, z1), z2, z3) -> ConsL(plus#2(z2, z0), zipwith_l#3(z3, z1)) fibs_2#1(zipwith_l, plus, tail_l, z0) -> ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))) zipwith_l#3(z0, z1) -> zipwith_l_f_xs_ys(plus, z0, z1) plus#2(0, z0) -> z0 plus#2(S(z0), z1) -> S(plus#2(z0, z1)) Tuples: COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, x1)), S(x2)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4)), S(x5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, x2)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[6])) COND_TAKE_L_N_XS(ConsL(x0, fibs_2(zipwith_l, plus, tail_l)), S(x1)) -> c2(COND_TAKE_L_N_XS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x1)) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0, x1)) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z1)), S(z2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z1), z2), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z1, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z2)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z2), z0, z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z2, bot[6])) PLUS#2(S(S(y0)), z1) -> c5(PLUS#2(S(y0), z1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x0)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x1), x2, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x0), x1, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x1, x2, x3), x4), x5, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x1, x2, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5), x6, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x0, x1, x2), x3), x4, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x0, x1, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4), x5, bot[0]) -> c7(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4), x5, bot[0]) -> c7(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4), x5, bot[0]) -> c13(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4), x5, bot[0]) -> c13(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4), x5, bot[0]) -> c14(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4), x5, bot[0]) -> c14(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4), x5, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5), x6, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[0]) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x4)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x5, bot[6]) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x5)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x0, bot[7]) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0)) COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), S(S(y0)), z3) -> c6(PLUS#2(S(S(y0)), z0)) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z4, bot[0])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z0), z1, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z0), z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z0, bot[7])) S tuples: COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, x2)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0, x1)) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z2)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z2), z0, z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z2, bot[6])) PLUS#2(S(S(y0)), z1) -> c5(PLUS#2(S(y0), z1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x0)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x0), x1, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5), x6, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x0, x1, x2), x3), x4, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x0, x1, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5), x6, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x5, bot[6]) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x5)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x0, bot[7]) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0)) COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), S(S(y0)), z3) -> c6(PLUS#2(S(S(y0)), z0)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z0), z1, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z0), z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z0, bot[7])) K tuples: COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(z1, z2, z3)), S(z4)) -> c3(COND_TAKE_L_N_XS(zipwith_l_f_xs_ys#1(z1, z2, z3, bot[0]), z4), ZIPWITH_L_F_XS_YS#1(z1, z2, z3, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, fibs_2(z1, z2, z3)), S(z4)) -> c2(COND_TAKE_L_N_XS(fibs_2#1(z1, z2, z3, bot[0]), z4)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x1)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x1), x2, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x1, x2, x3), x4), x5, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x1, x2, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4), x5, bot[0]) -> c7(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4), x5, bot[0]) -> c7(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4), x5, bot[0]) -> c13(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4), x5, bot[0]) -> c13(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4), x5, bot[0]) -> c14(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4), x5, bot[0]) -> c14(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4), x5, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[0]) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x4)) Defined Rule Symbols: zipwith_l_f_xs_ys#1_4, cond_zipwith_l_f_xs_ys_2, cond_zipwith_l_f_xs_ys_1_3, fibs_2#1_4, zipwith_l#3_2, plus#2_2 Defined Pair Symbols: COND_TAKE_L_N_XS_2, COND_ZIPWITH_L_F_XS_YS_2, PLUS#2_2, ZIPWITH_L_F_XS_YS#1_4, COND_ZIPWITH_L_F_XS_YS_1_3 Compound Symbols: c3_2, c3_1, c8_2, c8_1, c2_1, c9_1, c5_1, c10_1, c12_2, c_1, c1_1, c12_1, c4_1, c7_1, c13_1, c14_1, c11_1, c6_1 ---------------------------------------- (137) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4)), S(x5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4, bot[0])) by COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(y0, y1, y2)), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(y0, y1, y2)), z4, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(y0, y1, y2)), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(y0, y1, y2)), z4, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z3), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z3), z4, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z3), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z3), z4, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), z3), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), z3), z4, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, y0), z3), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, y0), z3), z4, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), y3), z3), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), y3), z3), z4, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), y3), z3), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), y3), z3), z4, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), z3), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), z3), z4, bot[0])) ---------------------------------------- (138) Obligation: Complexity Dependency Tuples Problem Rules: zipwith_l_f_xs_ys#1(plus, fibs, z0, z1) -> cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0) zipwith_l_f_xs_ys#1(plus, fibs_2(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3) zipwith_l_f_xs_ys#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), zipwith_l_f_xs_ys(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), fibs_2(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys_1(ConsL(z0, z1), z2, z3) -> ConsL(plus#2(z2, z0), zipwith_l#3(z3, z1)) fibs_2#1(zipwith_l, plus, tail_l, z0) -> ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))) zipwith_l#3(z0, z1) -> zipwith_l_f_xs_ys(plus, z0, z1) plus#2(0, z0) -> z0 plus#2(S(z0), z1) -> S(plus#2(z0, z1)) Tuples: COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, x1)), S(x2)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, x2)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[6])) COND_TAKE_L_N_XS(ConsL(x0, fibs_2(zipwith_l, plus, tail_l)), S(x1)) -> c2(COND_TAKE_L_N_XS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x1)) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0, x1)) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z1)), S(z2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z1), z2), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z1, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z2)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z2), z0, z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z2, bot[6])) PLUS#2(S(S(y0)), z1) -> c5(PLUS#2(S(y0), z1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x0)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x1), x2, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x0), x1, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x1, x2, x3), x4), x5, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x1, x2, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5), x6, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x0, x1, x2), x3), x4, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x0, x1, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4), x5, bot[0]) -> c7(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4), x5, bot[0]) -> c7(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4), x5, bot[0]) -> c13(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4), x5, bot[0]) -> c13(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4), x5, bot[0]) -> c14(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4), x5, bot[0]) -> c14(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4), x5, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5), x6, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[0]) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x4)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x5, bot[6]) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x5)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x0, bot[7]) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0)) COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), S(S(y0)), z3) -> c6(PLUS#2(S(S(y0)), z0)) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z4, bot[0])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z0), z1, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z0), z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z0, bot[7])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(y0, y1, y2)), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(y0, y1, y2)), z4, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(y0, y1, y2)), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(y0, y1, y2)), z4, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z3), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z3), z4, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z3), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z3), z4, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), z3), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), z3), z4, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, y0), z3), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, y0), z3), z4, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), y3), z3), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), y3), z3), z4, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), y3), z3), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), y3), z3), z4, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), z3), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), z3), z4, bot[0])) S tuples: COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, x2)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0, x1)) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z2)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z2), z0, z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z2, bot[6])) PLUS#2(S(S(y0)), z1) -> c5(PLUS#2(S(y0), z1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x0)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x0), x1, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5), x6, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x0, x1, x2), x3), x4, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x0, x1, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5), x6, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x5, bot[6]) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x5)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x0, bot[7]) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0)) COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), S(S(y0)), z3) -> c6(PLUS#2(S(S(y0)), z0)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z0), z1, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z0), z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z0, bot[7])) K tuples: COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(z1, z2, z3)), S(z4)) -> c3(COND_TAKE_L_N_XS(zipwith_l_f_xs_ys#1(z1, z2, z3, bot[0]), z4), ZIPWITH_L_F_XS_YS#1(z1, z2, z3, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, fibs_2(z1, z2, z3)), S(z4)) -> c2(COND_TAKE_L_N_XS(fibs_2#1(z1, z2, z3, bot[0]), z4)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x1)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x1), x2, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x1, x2, x3), x4), x5, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x1, x2, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4), x5, bot[0]) -> c7(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4), x5, bot[0]) -> c7(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4), x5, bot[0]) -> c13(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4), x5, bot[0]) -> c13(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4), x5, bot[0]) -> c14(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4), x5, bot[0]) -> c14(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4), x5, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[0]) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x4)) Defined Rule Symbols: zipwith_l_f_xs_ys#1_4, cond_zipwith_l_f_xs_ys_2, cond_zipwith_l_f_xs_ys_1_3, fibs_2#1_4, zipwith_l#3_2, plus#2_2 Defined Pair Symbols: COND_TAKE_L_N_XS_2, COND_ZIPWITH_L_F_XS_YS_2, PLUS#2_2, ZIPWITH_L_F_XS_YS#1_4, COND_ZIPWITH_L_F_XS_YS_1_3 Compound Symbols: c3_2, c3_1, c8_2, c8_1, c2_1, c9_1, c5_1, c10_1, c12_2, c_1, c1_1, c12_1, c4_1, c7_1, c13_1, c14_1, c11_1, c6_1 ---------------------------------------- (139) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[6])) by COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z5, bot[6])) ---------------------------------------- (140) Obligation: Complexity Dependency Tuples Problem Rules: zipwith_l_f_xs_ys#1(plus, fibs, z0, z1) -> cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0) zipwith_l_f_xs_ys#1(plus, fibs_2(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3) zipwith_l_f_xs_ys#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), zipwith_l_f_xs_ys(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), fibs_2(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys_1(ConsL(z0, z1), z2, z3) -> ConsL(plus#2(z2, z0), zipwith_l#3(z3, z1)) fibs_2#1(zipwith_l, plus, tail_l, z0) -> ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))) zipwith_l#3(z0, z1) -> zipwith_l_f_xs_ys(plus, z0, z1) plus#2(0, z0) -> z0 plus#2(S(z0), z1) -> S(plus#2(z0, z1)) Tuples: COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, x1)), S(x2)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, x2)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[6])) COND_TAKE_L_N_XS(ConsL(x0, fibs_2(zipwith_l, plus, tail_l)), S(x1)) -> c2(COND_TAKE_L_N_XS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x1)) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0, x1)) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z1)), S(z2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z1), z2), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z1, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z2)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z2), z0, z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z2, bot[6])) PLUS#2(S(S(y0)), z1) -> c5(PLUS#2(S(y0), z1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x0)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x1), x2, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x0), x1, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x1, x2, x3), x4), x5, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x1, x2, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5), x6, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x0, x1, x2), x3), x4, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x0, x1, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4), x5, bot[0]) -> c7(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4), x5, bot[0]) -> c7(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4), x5, bot[0]) -> c13(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4), x5, bot[0]) -> c13(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4), x5, bot[0]) -> c14(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4), x5, bot[0]) -> c14(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4), x5, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5), x6, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[0]) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x4)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x5, bot[6]) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x5)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x0, bot[7]) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0)) COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), S(S(y0)), z3) -> c6(PLUS#2(S(S(y0)), z0)) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z4, bot[0])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z0), z1, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z0), z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z0, bot[7])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(y0, y1, y2)), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(y0, y1, y2)), z4, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(y0, y1, y2)), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(y0, y1, y2)), z4, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z3), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z3), z4, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z3), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z3), z4, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), z3), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), z3), z4, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, y0), z3), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, y0), z3), z4, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), y3), z3), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), y3), z3), z4, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), y3), z3), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), y3), z3), z4, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), z3), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), z3), z4, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z5, bot[6])) S tuples: COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, x2)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0, x1)) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z2)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z2), z0, z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z2, bot[6])) PLUS#2(S(S(y0)), z1) -> c5(PLUS#2(S(y0), z1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x0)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x0), x1, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5), x6, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x0, x1, x2), x3), x4, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x0, x1, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5), x6, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x5, bot[6]) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x5)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x0, bot[7]) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0)) COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), S(S(y0)), z3) -> c6(PLUS#2(S(S(y0)), z0)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z0), z1, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z0), z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z0, bot[7])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z5, bot[6])) K tuples: COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(z1, z2, z3)), S(z4)) -> c3(COND_TAKE_L_N_XS(zipwith_l_f_xs_ys#1(z1, z2, z3, bot[0]), z4), ZIPWITH_L_F_XS_YS#1(z1, z2, z3, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, fibs_2(z1, z2, z3)), S(z4)) -> c2(COND_TAKE_L_N_XS(fibs_2#1(z1, z2, z3, bot[0]), z4)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x1)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x1), x2, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x1, x2, x3), x4), x5, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x1, x2, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4), x5, bot[0]) -> c7(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4), x5, bot[0]) -> c7(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4), x5, bot[0]) -> c13(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4), x5, bot[0]) -> c13(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4), x5, bot[0]) -> c14(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4), x5, bot[0]) -> c14(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4), x5, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[0]) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x4)) Defined Rule Symbols: zipwith_l_f_xs_ys#1_4, cond_zipwith_l_f_xs_ys_2, cond_zipwith_l_f_xs_ys_1_3, fibs_2#1_4, zipwith_l#3_2, plus#2_2 Defined Pair Symbols: COND_TAKE_L_N_XS_2, COND_ZIPWITH_L_F_XS_YS_2, PLUS#2_2, ZIPWITH_L_F_XS_YS#1_4, COND_ZIPWITH_L_F_XS_YS_1_3 Compound Symbols: c3_2, c3_1, c8_2, c8_1, c2_1, c9_1, c5_1, c10_1, c12_2, c_1, c1_1, c12_1, c4_1, c7_1, c13_1, c14_1, c11_1, c6_1 ---------------------------------------- (141) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[6])) by COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(y0, y1, y2)), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(y0, y1, y2)), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(y0, y1, y2)), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(y0, y1, y2)), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, y0), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, y0), z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), y3), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), y3), z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), y3), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), y3), z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z4), z5, bot[6])) ---------------------------------------- (142) Obligation: Complexity Dependency Tuples Problem Rules: zipwith_l_f_xs_ys#1(plus, fibs, z0, z1) -> cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0) zipwith_l_f_xs_ys#1(plus, fibs_2(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3) zipwith_l_f_xs_ys#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), zipwith_l_f_xs_ys(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), fibs_2(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys_1(ConsL(z0, z1), z2, z3) -> ConsL(plus#2(z2, z0), zipwith_l#3(z3, z1)) fibs_2#1(zipwith_l, plus, tail_l, z0) -> ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))) zipwith_l#3(z0, z1) -> zipwith_l_f_xs_ys(plus, z0, z1) plus#2(0, z0) -> z0 plus#2(S(z0), z1) -> S(plus#2(z0, z1)) Tuples: COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, x1)), S(x2)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, x2)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5, bot[6])) COND_TAKE_L_N_XS(ConsL(x0, fibs_2(zipwith_l, plus, tail_l)), S(x1)) -> c2(COND_TAKE_L_N_XS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x1)) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0, x1)) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z1)), S(z2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z1), z2), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z1, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z2)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z2), z0, z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z2, bot[6])) PLUS#2(S(S(y0)), z1) -> c5(PLUS#2(S(y0), z1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x0)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x1), x2, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x0), x1, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x1, x2, x3), x4), x5, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x1, x2, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5), x6, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x0, x1, x2), x3), x4, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x0, x1, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4), x5, bot[0]) -> c7(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4), x5, bot[0]) -> c7(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4), x5, bot[0]) -> c13(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4), x5, bot[0]) -> c13(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4), x5, bot[0]) -> c14(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4), x5, bot[0]) -> c14(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4), x5, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5), x6, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[0]) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x4)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x5, bot[6]) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x5)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x0, bot[7]) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0)) COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), S(S(y0)), z3) -> c6(PLUS#2(S(S(y0)), z0)) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z4, bot[0])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z0), z1, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z0), z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z0, bot[7])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(y0, y1, y2)), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(y0, y1, y2)), z4, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(y0, y1, y2)), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(y0, y1, y2)), z4, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z3), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z3), z4, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z3), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z3), z4, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), z3), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), z3), z4, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, y0), z3), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, y0), z3), z4, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), y3), z3), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), y3), z3), z4, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), y3), z3), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), y3), z3), z4, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), z3), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), z3), z4, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(y0, y1, y2)), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(y0, y1, y2)), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(y0, y1, y2)), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(y0, y1, y2)), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, y0), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, y0), z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), y3), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), y3), z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), y3), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), y3), z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z4), z5, bot[6])) S tuples: COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, x2)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0, x1)) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z2)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z2), z0, z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z2, bot[6])) PLUS#2(S(S(y0)), z1) -> c5(PLUS#2(S(y0), z1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x0)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x0), x1, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5), x6, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x0, x1, x2), x3), x4, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x0, x1, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5), x6, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x5, bot[6]) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x5)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x0, bot[7]) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0)) COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), S(S(y0)), z3) -> c6(PLUS#2(S(S(y0)), z0)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z0), z1, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z0), z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z0, bot[7])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(y0, y1, y2)), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(y0, y1, y2)), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(y0, y1, y2)), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(y0, y1, y2)), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, y0), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, y0), z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), y3), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), y3), z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), y3), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), y3), z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z4), z5, bot[6])) K tuples: COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(z1, z2, z3)), S(z4)) -> c3(COND_TAKE_L_N_XS(zipwith_l_f_xs_ys#1(z1, z2, z3, bot[0]), z4), ZIPWITH_L_F_XS_YS#1(z1, z2, z3, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, fibs_2(z1, z2, z3)), S(z4)) -> c2(COND_TAKE_L_N_XS(fibs_2#1(z1, z2, z3, bot[0]), z4)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x1)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x1), x2, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x1, x2, x3), x4), x5, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x1, x2, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4), x5, bot[0]) -> c7(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4), x5, bot[0]) -> c7(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4), x5, bot[0]) -> c13(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4), x5, bot[0]) -> c13(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4), x5, bot[0]) -> c14(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4), x5, bot[0]) -> c14(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4), x5, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[0]) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x4)) Defined Rule Symbols: zipwith_l_f_xs_ys#1_4, cond_zipwith_l_f_xs_ys_2, cond_zipwith_l_f_xs_ys_1_3, fibs_2#1_4, zipwith_l#3_2, plus#2_2 Defined Pair Symbols: COND_TAKE_L_N_XS_2, COND_ZIPWITH_L_F_XS_YS_2, PLUS#2_2, ZIPWITH_L_F_XS_YS#1_4, COND_ZIPWITH_L_F_XS_YS_1_3 Compound Symbols: c3_2, c3_1, c8_2, c8_1, c2_1, c9_1, c5_1, c10_1, c12_2, c_1, c1_1, c12_1, c4_1, c7_1, c13_1, c14_1, c11_1, c6_1 ---------------------------------------- (143) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace COND_TAKE_L_N_XS(ConsL(x0, fibs_2(zipwith_l, plus, tail_l)), S(x1)) -> c2(COND_TAKE_L_N_XS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x1)) by COND_TAKE_L_N_XS(ConsL(z0, fibs_2(zipwith_l, plus, tail_l)), S(S(y4))) -> c2(COND_TAKE_L_N_XS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), S(y4))) ---------------------------------------- (144) Obligation: Complexity Dependency Tuples Problem Rules: zipwith_l_f_xs_ys#1(plus, fibs, z0, z1) -> cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0) zipwith_l_f_xs_ys#1(plus, fibs_2(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3) zipwith_l_f_xs_ys#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), zipwith_l_f_xs_ys(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), fibs_2(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys_1(ConsL(z0, z1), z2, z3) -> ConsL(plus#2(z2, z0), zipwith_l#3(z3, z1)) fibs_2#1(zipwith_l, plus, tail_l, z0) -> ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))) zipwith_l#3(z0, z1) -> zipwith_l_f_xs_ys(plus, z0, z1) plus#2(0, z0) -> z0 plus#2(S(z0), z1) -> S(plus#2(z0, z1)) Tuples: COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, x1)), S(x2)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, x2)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0, x1)) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z1)), S(z2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z1), z2), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z1, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z2)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z2), z0, z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z2, bot[6])) PLUS#2(S(S(y0)), z1) -> c5(PLUS#2(S(y0), z1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x0)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x1), x2, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x0), x1, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x1, x2, x3), x4), x5, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x1, x2, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5), x6, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x0, x1, x2), x3), x4, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x0, x1, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4), x5, bot[0]) -> c7(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4), x5, bot[0]) -> c7(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4), x5, bot[0]) -> c13(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4), x5, bot[0]) -> c13(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4), x5, bot[0]) -> c14(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4), x5, bot[0]) -> c14(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4), x5, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5), x6, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[0]) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x4)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x5, bot[6]) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x5)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x0, bot[7]) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0)) COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), S(S(y0)), z3) -> c6(PLUS#2(S(S(y0)), z0)) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z4, bot[0])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z0), z1, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z0), z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z0, bot[7])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(y0, y1, y2)), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(y0, y1, y2)), z4, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(y0, y1, y2)), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(y0, y1, y2)), z4, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z3), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z3), z4, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z3), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z3), z4, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), z3), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), z3), z4, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, y0), z3), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, y0), z3), z4, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), y3), z3), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), y3), z3), z4, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), y3), z3), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), y3), z3), z4, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), z3), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), z3), z4, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(y0, y1, y2)), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(y0, y1, y2)), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(y0, y1, y2)), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(y0, y1, y2)), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, y0), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, y0), z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), y3), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), y3), z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), y3), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), y3), z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z4), z5, bot[6])) COND_TAKE_L_N_XS(ConsL(z0, fibs_2(zipwith_l, plus, tail_l)), S(S(y4))) -> c2(COND_TAKE_L_N_XS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), S(y4))) S tuples: COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, x2)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0, x1)) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z2)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z2), z0, z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z2, bot[6])) PLUS#2(S(S(y0)), z1) -> c5(PLUS#2(S(y0), z1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x0)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x0), x1, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5), x6, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x0, x1, x2), x3), x4, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x0, x1, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5), x6, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x5, bot[6]) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x5)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x0, bot[7]) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0)) COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), S(S(y0)), z3) -> c6(PLUS#2(S(S(y0)), z0)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z0), z1, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z0), z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z0, bot[7])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(y0, y1, y2)), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(y0, y1, y2)), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(y0, y1, y2)), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(y0, y1, y2)), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, y0), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, y0), z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), y3), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), y3), z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), y3), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), y3), z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z4), z5, bot[6])) K tuples: COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(z1, z2, z3)), S(z4)) -> c3(COND_TAKE_L_N_XS(zipwith_l_f_xs_ys#1(z1, z2, z3, bot[0]), z4), ZIPWITH_L_F_XS_YS#1(z1, z2, z3, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, fibs_2(z1, z2, z3)), S(z4)) -> c2(COND_TAKE_L_N_XS(fibs_2#1(z1, z2, z3, bot[0]), z4)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x1)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x1), x2, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x1, x2, x3), x4), x5, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x1, x2, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4), x5, bot[0]) -> c7(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4), x5, bot[0]) -> c7(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4), x5, bot[0]) -> c13(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4), x5, bot[0]) -> c13(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4), x5, bot[0]) -> c14(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4), x5, bot[0]) -> c14(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4), x5, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[0]) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x4)) Defined Rule Symbols: zipwith_l_f_xs_ys#1_4, cond_zipwith_l_f_xs_ys_2, cond_zipwith_l_f_xs_ys_1_3, fibs_2#1_4, zipwith_l#3_2, plus#2_2 Defined Pair Symbols: COND_TAKE_L_N_XS_2, COND_ZIPWITH_L_F_XS_YS_2, PLUS#2_2, ZIPWITH_L_F_XS_YS#1_4, COND_ZIPWITH_L_F_XS_YS_1_3 Compound Symbols: c3_2, c3_1, c8_2, c8_1, c9_1, c5_1, c10_1, c12_2, c_1, c1_1, c12_1, c4_1, c7_1, c13_1, c14_1, c11_1, c6_1, c2_1 ---------------------------------------- (145) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0, x1)) by COND_ZIPWITH_L_F_XS_YS(ConsL(S(S(y2)), z1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), S(S(y2)), z1)) ---------------------------------------- (146) Obligation: Complexity Dependency Tuples Problem Rules: zipwith_l_f_xs_ys#1(plus, fibs, z0, z1) -> cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0) zipwith_l_f_xs_ys#1(plus, fibs_2(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3) zipwith_l_f_xs_ys#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), zipwith_l_f_xs_ys(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), fibs_2(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys_1(ConsL(z0, z1), z2, z3) -> ConsL(plus#2(z2, z0), zipwith_l#3(z3, z1)) fibs_2#1(zipwith_l, plus, tail_l, z0) -> ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))) zipwith_l#3(z0, z1) -> zipwith_l_f_xs_ys(plus, z0, z1) plus#2(0, z0) -> z0 plus#2(S(z0), z1) -> S(plus#2(z0, z1)) Tuples: COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, x1)), S(x2)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, x2)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5, bot[6])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z1)), S(z2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z1), z2), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z1, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z2)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z2), z0, z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z2, bot[6])) PLUS#2(S(S(y0)), z1) -> c5(PLUS#2(S(y0), z1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x0)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x1), x2, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x0), x1, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x1, x2, x3), x4), x5, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x1, x2, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5), x6, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x0, x1, x2), x3), x4, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x0, x1, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4), x5, bot[0]) -> c7(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4), x5, bot[0]) -> c7(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4), x5, bot[0]) -> c13(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4), x5, bot[0]) -> c13(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4), x5, bot[0]) -> c14(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4), x5, bot[0]) -> c14(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4), x5, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5), x6, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[0]) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x4)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x5, bot[6]) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x5)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x0, bot[7]) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0)) COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), S(S(y0)), z3) -> c6(PLUS#2(S(S(y0)), z0)) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z4, bot[0])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z0), z1, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z0), z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z0, bot[7])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(y0, y1, y2)), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(y0, y1, y2)), z4, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(y0, y1, y2)), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(y0, y1, y2)), z4, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z3), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z3), z4, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z3), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z3), z4, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), z3), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), z3), z4, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, y0), z3), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, y0), z3), z4, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), y3), z3), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), y3), z3), z4, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), y3), z3), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), y3), z3), z4, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), z3), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), z3), z4, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(y0, y1, y2)), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(y0, y1, y2)), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(y0, y1, y2)), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(y0, y1, y2)), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, y0), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, y0), z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), y3), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), y3), z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), y3), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), y3), z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z4), z5, bot[6])) COND_TAKE_L_N_XS(ConsL(z0, fibs_2(zipwith_l, plus, tail_l)), S(S(y4))) -> c2(COND_TAKE_L_N_XS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), S(y4))) COND_ZIPWITH_L_F_XS_YS(ConsL(S(S(y2)), z1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), S(S(y2)), z1)) S tuples: COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, x2)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z2)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z2), z0, z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z2, bot[6])) PLUS#2(S(S(y0)), z1) -> c5(PLUS#2(S(y0), z1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x0)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x0), x1, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5), x6, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x0, x1, x2), x3), x4, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x0, x1, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5), x6, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x5, bot[6]) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x5)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x0, bot[7]) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0)) COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), S(S(y0)), z3) -> c6(PLUS#2(S(S(y0)), z0)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z0), z1, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z0), z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z0, bot[7])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(y0, y1, y2)), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(y0, y1, y2)), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(y0, y1, y2)), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(y0, y1, y2)), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, y0), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, y0), z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), y3), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), y3), z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), y3), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), y3), z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(S(S(y2)), z1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), S(S(y2)), z1)) K tuples: COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(z1, z2, z3)), S(z4)) -> c3(COND_TAKE_L_N_XS(zipwith_l_f_xs_ys#1(z1, z2, z3, bot[0]), z4), ZIPWITH_L_F_XS_YS#1(z1, z2, z3, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, fibs_2(z1, z2, z3)), S(z4)) -> c2(COND_TAKE_L_N_XS(fibs_2#1(z1, z2, z3, bot[0]), z4)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x1)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x1), x2, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x1, x2, x3), x4), x5, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x1, x2, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4), x5, bot[0]) -> c7(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4), x5, bot[0]) -> c7(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4), x5, bot[0]) -> c13(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4), x5, bot[0]) -> c13(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4), x5, bot[0]) -> c14(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4), x5, bot[0]) -> c14(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4), x5, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[0]) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x4)) Defined Rule Symbols: zipwith_l_f_xs_ys#1_4, cond_zipwith_l_f_xs_ys_2, cond_zipwith_l_f_xs_ys_1_3, fibs_2#1_4, zipwith_l#3_2, plus#2_2 Defined Pair Symbols: COND_TAKE_L_N_XS_2, COND_ZIPWITH_L_F_XS_YS_2, PLUS#2_2, ZIPWITH_L_F_XS_YS#1_4, COND_ZIPWITH_L_F_XS_YS_1_3 Compound Symbols: c3_2, c3_1, c8_2, c8_1, c5_1, c10_1, c12_2, c_1, c1_1, c12_1, c4_1, c7_1, c13_1, c14_1, c11_1, c6_1, c2_1, c9_1 ---------------------------------------- (147) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing nodes: ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), fibs_2(x2, x3, x4))) ---------------------------------------- (148) Obligation: Complexity Dependency Tuples Problem Rules: zipwith_l_f_xs_ys#1(plus, fibs, z0, z1) -> cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0) zipwith_l_f_xs_ys#1(plus, fibs_2(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3) zipwith_l_f_xs_ys#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), zipwith_l_f_xs_ys(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), fibs_2(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys_1(ConsL(z0, z1), z2, z3) -> ConsL(plus#2(z2, z0), zipwith_l#3(z3, z1)) fibs_2#1(zipwith_l, plus, tail_l, z0) -> ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))) zipwith_l#3(z0, z1) -> zipwith_l_f_xs_ys(plus, z0, z1) plus#2(0, z0) -> z0 plus#2(S(z0), z1) -> S(plus#2(z0, z1)) Tuples: COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, x1)), S(x2)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, x2)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5, bot[6])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z1)), S(z2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z1), z2), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z1, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z2)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z2), z0, z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z2, bot[6])) PLUS#2(S(S(y0)), z1) -> c5(PLUS#2(S(y0), z1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x0)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x1), x2, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x0), x1, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x1, x2, x3), x4), x5, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x1, x2, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5), x6, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x0, x1, x2), x3), x4, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x0, x1, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4), x5, bot[0]) -> c7(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4), x5, bot[0]) -> c7(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4), x5, bot[0]) -> c13(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4), x5, bot[0]) -> c13(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4), x5, bot[0]) -> c14(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4), x5, bot[0]) -> c14(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4), x5, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5), x6, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[0]) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x4)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x5, bot[6]) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x5)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x0, bot[7]) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0)) COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), S(S(y0)), z3) -> c6(PLUS#2(S(S(y0)), z0)) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z4, bot[0])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z0), z1, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z0), z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z0, bot[7])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(y0, y1, y2)), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(y0, y1, y2)), z4, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(y0, y1, y2)), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(y0, y1, y2)), z4, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z3), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z3), z4, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z3), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z3), z4, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), z3), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), z3), z4, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, y0), z3), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, y0), z3), z4, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), y3), z3), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), y3), z3), z4, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), y3), z3), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), y3), z3), z4, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), z3), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), z3), z4, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(y0, y1, y2)), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(y0, y1, y2)), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(y0, y1, y2)), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(y0, y1, y2)), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, y0), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, y0), z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), y3), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), y3), z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), y3), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), y3), z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z4), z5, bot[6])) COND_TAKE_L_N_XS(ConsL(z0, fibs_2(zipwith_l, plus, tail_l)), S(S(y4))) -> c2(COND_TAKE_L_N_XS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), S(y4))) COND_ZIPWITH_L_F_XS_YS(ConsL(S(S(y2)), z1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), S(S(y2)), z1)) S tuples: COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, x2)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z2)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z2), z0, z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z2, bot[6])) PLUS#2(S(S(y0)), z1) -> c5(PLUS#2(S(y0), z1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x0)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x0), x1, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5), x6, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x0, x1, x2), x3), x4, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x0, x1, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5), x6, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x5, bot[6]) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x5)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x0, bot[7]) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0)) COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), S(S(y0)), z3) -> c6(PLUS#2(S(S(y0)), z0)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z0), z1, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z0), z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z0, bot[7])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(y0, y1, y2)), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(y0, y1, y2)), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(y0, y1, y2)), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(y0, y1, y2)), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, y0), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, y0), z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), y3), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), y3), z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), y3), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), y3), z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(S(S(y2)), z1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), S(S(y2)), z1)) K tuples: ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x1)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x1), x2, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x1, x2, x3), x4), x5, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x1, x2, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4), x5, bot[0]) -> c7(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4), x5, bot[0]) -> c7(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4), x5, bot[0]) -> c13(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4), x5, bot[0]) -> c13(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4), x5, bot[0]) -> c14(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4), x5, bot[0]) -> c14(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4), x5, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[0]) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x4)) Defined Rule Symbols: zipwith_l_f_xs_ys#1_4, cond_zipwith_l_f_xs_ys_2, cond_zipwith_l_f_xs_ys_1_3, fibs_2#1_4, zipwith_l#3_2, plus#2_2 Defined Pair Symbols: COND_TAKE_L_N_XS_2, COND_ZIPWITH_L_F_XS_YS_2, PLUS#2_2, ZIPWITH_L_F_XS_YS#1_4, COND_ZIPWITH_L_F_XS_YS_1_3 Compound Symbols: c3_2, c3_1, c8_2, c8_1, c5_1, c10_1, c12_2, c_1, c1_1, c12_1, c4_1, c7_1, c13_1, c14_1, c11_1, c6_1, c2_1, c9_1 ---------------------------------------- (149) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace PLUS#2(S(S(y0)), z1) -> c5(PLUS#2(S(y0), z1)) by PLUS#2(S(S(S(y0))), z1) -> c5(PLUS#2(S(S(y0)), z1)) ---------------------------------------- (150) Obligation: Complexity Dependency Tuples Problem Rules: zipwith_l_f_xs_ys#1(plus, fibs, z0, z1) -> cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0) zipwith_l_f_xs_ys#1(plus, fibs_2(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3) zipwith_l_f_xs_ys#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), zipwith_l_f_xs_ys(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), fibs_2(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys_1(ConsL(z0, z1), z2, z3) -> ConsL(plus#2(z2, z0), zipwith_l#3(z3, z1)) fibs_2#1(zipwith_l, plus, tail_l, z0) -> ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))) zipwith_l#3(z0, z1) -> zipwith_l_f_xs_ys(plus, z0, z1) plus#2(0, z0) -> z0 plus#2(S(z0), z1) -> S(plus#2(z0, z1)) Tuples: COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, x1)), S(x2)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, x2)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5, bot[6])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z1)), S(z2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z1), z2), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z1, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z2)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z2), z0, z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z2, bot[6])) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x0)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x1), x2, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x0), x1, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x1, x2, x3), x4), x5, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x1, x2, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5), x6, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x0, x1, x2), x3), x4, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x0, x1, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4), x5, bot[0]) -> c7(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4), x5, bot[0]) -> c7(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4), x5, bot[0]) -> c13(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4), x5, bot[0]) -> c13(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4), x5, bot[0]) -> c14(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4), x5, bot[0]) -> c14(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4), x5, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5), x6, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[0]) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x4)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x5, bot[6]) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x5)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x0, bot[7]) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0)) COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), S(S(y0)), z3) -> c6(PLUS#2(S(S(y0)), z0)) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z4, bot[0])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z0), z1, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z0), z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z0, bot[7])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(y0, y1, y2)), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(y0, y1, y2)), z4, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(y0, y1, y2)), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(y0, y1, y2)), z4, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z3), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z3), z4, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z3), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z3), z4, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), z3), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), z3), z4, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, y0), z3), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, y0), z3), z4, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), y3), z3), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), y3), z3), z4, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), y3), z3), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), y3), z3), z4, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), z3), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), z3), z4, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(y0, y1, y2)), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(y0, y1, y2)), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(y0, y1, y2)), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(y0, y1, y2)), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, y0), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, y0), z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), y3), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), y3), z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), y3), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), y3), z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z4), z5, bot[6])) COND_TAKE_L_N_XS(ConsL(z0, fibs_2(zipwith_l, plus, tail_l)), S(S(y4))) -> c2(COND_TAKE_L_N_XS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), S(y4))) COND_ZIPWITH_L_F_XS_YS(ConsL(S(S(y2)), z1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), S(S(y2)), z1)) PLUS#2(S(S(S(y0))), z1) -> c5(PLUS#2(S(S(y0)), z1)) S tuples: COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, x2)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z2)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z2), z0, z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z2, bot[6])) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x0)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x0), x1, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5), x6, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x0, x1, x2), x3), x4, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x0, x1, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5), x6, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x5, bot[6]) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x5)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x0, bot[7]) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0)) COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), S(S(y0)), z3) -> c6(PLUS#2(S(S(y0)), z0)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z0), z1, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z0), z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z0, bot[7])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(y0, y1, y2)), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(y0, y1, y2)), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(y0, y1, y2)), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(y0, y1, y2)), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, y0), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, y0), z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), y3), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), y3), z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), y3), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), y3), z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(S(S(y2)), z1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), S(S(y2)), z1)) PLUS#2(S(S(S(y0))), z1) -> c5(PLUS#2(S(S(y0)), z1)) K tuples: ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x1)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x1), x2, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x1, x2, x3), x4), x5, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x1, x2, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4), x5, bot[0]) -> c7(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4), x5, bot[0]) -> c7(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4), x5, bot[0]) -> c13(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4), x5, bot[0]) -> c13(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4), x5, bot[0]) -> c14(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4), x5, bot[0]) -> c14(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4), x5, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[0]) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x4)) Defined Rule Symbols: zipwith_l_f_xs_ys#1_4, cond_zipwith_l_f_xs_ys_2, cond_zipwith_l_f_xs_ys_1_3, fibs_2#1_4, zipwith_l#3_2, plus#2_2 Defined Pair Symbols: COND_TAKE_L_N_XS_2, COND_ZIPWITH_L_F_XS_YS_2, ZIPWITH_L_F_XS_YS#1_4, COND_ZIPWITH_L_F_XS_YS_1_3, PLUS#2_2 Compound Symbols: c3_2, c3_1, c8_2, c8_1, c10_1, c12_2, c_1, c1_1, c12_1, c4_1, c7_1, c13_1, c14_1, c11_1, c6_1, c2_1, c9_1, c5_1 ---------------------------------------- (151) CdtRewritingProof (BOTH BOUNDS(ID, ID)) Used rewriting to replace ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x3, bot[7])) by ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z0), z1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z0), z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z0, bot[7])) ---------------------------------------- (152) Obligation: Complexity Dependency Tuples Problem Rules: zipwith_l_f_xs_ys#1(plus, fibs, z0, z1) -> cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0) zipwith_l_f_xs_ys#1(plus, fibs_2(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3) zipwith_l_f_xs_ys#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), zipwith_l_f_xs_ys(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), fibs_2(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys_1(ConsL(z0, z1), z2, z3) -> ConsL(plus#2(z2, z0), zipwith_l#3(z3, z1)) fibs_2#1(zipwith_l, plus, tail_l, z0) -> ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))) zipwith_l#3(z0, z1) -> zipwith_l_f_xs_ys(plus, z0, z1) plus#2(0, z0) -> z0 plus#2(S(z0), z1) -> S(plus#2(z0, z1)) Tuples: COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, x1)), S(x2)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, x2)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5, bot[6])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z1)), S(z2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z1), z2), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z1, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z2)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z2), z0, z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z2, bot[6])) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x0)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x1), x2, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x0), x1, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x1, x2, x3), x4), x5, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x1, x2, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5), x6, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x0, x1, x2), x3), x4, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x0, x1, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4), x5, bot[0]) -> c7(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4), x5, bot[0]) -> c7(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4), x5, bot[0]) -> c13(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4), x5, bot[0]) -> c13(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4), x5, bot[0]) -> c14(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4), x5, bot[0]) -> c14(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4), x5, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5), x6, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[0]) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x4)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x5, bot[6]) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x5)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x0, bot[7]) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0)) COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), S(S(y0)), z3) -> c6(PLUS#2(S(S(y0)), z0)) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z4, bot[0])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z0), z1, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z0), z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z0, bot[7])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(y0, y1, y2)), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(y0, y1, y2)), z4, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(y0, y1, y2)), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(y0, y1, y2)), z4, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z3), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z3), z4, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z3), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z3), z4, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), z3), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), z3), z4, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, y0), z3), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, y0), z3), z4, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), y3), z3), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), y3), z3), z4, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), y3), z3), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), y3), z3), z4, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), z3), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), z3), z4, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(y0, y1, y2)), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(y0, y1, y2)), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(y0, y1, y2)), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(y0, y1, y2)), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, y0), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, y0), z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), y3), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), y3), z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), y3), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), y3), z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z4), z5, bot[6])) COND_TAKE_L_N_XS(ConsL(z0, fibs_2(zipwith_l, plus, tail_l)), S(S(y4))) -> c2(COND_TAKE_L_N_XS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), S(y4))) COND_ZIPWITH_L_F_XS_YS(ConsL(S(S(y2)), z1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), S(S(y2)), z1)) PLUS#2(S(S(S(y0))), z1) -> c5(PLUS#2(S(S(y0)), z1)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z0), z1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z0), z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z0, bot[7])) S tuples: COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, x2)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z2)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z2), z0, z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z2, bot[6])) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x0)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x0), x1, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5), x6, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x0, x1, x2), x3), x4, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x0, x1, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5), x6, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x5, bot[6]) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x5)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x0, bot[7]) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0)) COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), S(S(y0)), z3) -> c6(PLUS#2(S(S(y0)), z0)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z0), z1, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z0), z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z0, bot[7])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(y0, y1, y2)), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(y0, y1, y2)), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(y0, y1, y2)), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(y0, y1, y2)), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, y0), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, y0), z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), y3), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), y3), z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), y3), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), y3), z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(S(S(y2)), z1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), S(S(y2)), z1)) PLUS#2(S(S(S(y0))), z1) -> c5(PLUS#2(S(S(y0)), z1)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z0), z1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z0), z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z0, bot[7])) K tuples: ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x1)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x1), x2, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x1, x2, x3), x4), x5, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x1, x2, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4), x5, bot[0]) -> c7(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4), x5, bot[0]) -> c7(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4), x5, bot[0]) -> c13(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4), x5, bot[0]) -> c13(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4), x5, bot[0]) -> c14(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4), x5, bot[0]) -> c14(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4), x5, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[0]) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x4)) Defined Rule Symbols: zipwith_l_f_xs_ys#1_4, cond_zipwith_l_f_xs_ys_2, cond_zipwith_l_f_xs_ys_1_3, fibs_2#1_4, zipwith_l#3_2, plus#2_2 Defined Pair Symbols: COND_TAKE_L_N_XS_2, COND_ZIPWITH_L_F_XS_YS_2, ZIPWITH_L_F_XS_YS#1_4, COND_ZIPWITH_L_F_XS_YS_1_3, PLUS#2_2 Compound Symbols: c3_2, c3_1, c8_2, c8_1, c10_1, c12_2, c_1, c1_1, c12_1, c4_1, c7_1, c13_1, c14_1, c11_1, c6_1, c2_1, c9_1, c5_1 ---------------------------------------- (153) CdtRewritingProof (BOTH BOUNDS(ID, ID)) Used rewriting to replace ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x4), x5)) by ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z0), z1, bot[0]) -> c4(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z0), z1)) ---------------------------------------- (154) Obligation: Complexity Dependency Tuples Problem Rules: zipwith_l_f_xs_ys#1(plus, fibs, z0, z1) -> cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0) zipwith_l_f_xs_ys#1(plus, fibs_2(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3) zipwith_l_f_xs_ys#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), zipwith_l_f_xs_ys(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), fibs_2(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys_1(ConsL(z0, z1), z2, z3) -> ConsL(plus#2(z2, z0), zipwith_l#3(z3, z1)) fibs_2#1(zipwith_l, plus, tail_l, z0) -> ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))) zipwith_l#3(z0, z1) -> zipwith_l_f_xs_ys(plus, z0, z1) plus#2(0, z0) -> z0 plus#2(S(z0), z1) -> S(plus#2(z0, z1)) Tuples: COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, x1)), S(x2)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, x2)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5, bot[6])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z1)), S(z2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z1), z2), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z1, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z2)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z2), z0, z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z2, bot[6])) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x0)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x1), x2, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x0), x1, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x1, x2, x3), x4), x5, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x1, x2, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5), x6, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x0, x1, x2), x3), x4, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x0, x1, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4), x5, bot[0]) -> c7(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4), x5, bot[0]) -> c7(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4), x5, bot[0]) -> c13(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4), x5, bot[0]) -> c13(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4), x5, bot[0]) -> c14(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4), x5, bot[0]) -> c14(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4), x5, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5), x6, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[0]) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x4)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x5, bot[6]) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x5)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x0, bot[7]) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0)) COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), S(S(y0)), z3) -> c6(PLUS#2(S(S(y0)), z0)) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z4, bot[0])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z0), z1, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z0), z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z0, bot[7])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(y0, y1, y2)), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(y0, y1, y2)), z4, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(y0, y1, y2)), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(y0, y1, y2)), z4, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z3), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z3), z4, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z3), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z3), z4, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), z3), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), z3), z4, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, y0), z3), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, y0), z3), z4, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), y3), z3), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), y3), z3), z4, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), y3), z3), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), y3), z3), z4, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), z3), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), z3), z4, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(y0, y1, y2)), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(y0, y1, y2)), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(y0, y1, y2)), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(y0, y1, y2)), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, y0), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, y0), z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), y3), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), y3), z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), y3), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), y3), z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z4), z5, bot[6])) COND_TAKE_L_N_XS(ConsL(z0, fibs_2(zipwith_l, plus, tail_l)), S(S(y4))) -> c2(COND_TAKE_L_N_XS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), S(y4))) COND_ZIPWITH_L_F_XS_YS(ConsL(S(S(y2)), z1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), S(S(y2)), z1)) PLUS#2(S(S(S(y0))), z1) -> c5(PLUS#2(S(S(y0)), z1)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z0), z1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z0), z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z0), z1, bot[0]) -> c4(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z0), z1)) S tuples: COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, x2)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z2)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z2), z0, z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z2, bot[6])) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x0)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x0), x1, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5), x6, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x0, x1, x2), x3), x4, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x0, x1, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5), x6, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x5, bot[6]) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x5)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x0, bot[7]) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0)) COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), S(S(y0)), z3) -> c6(PLUS#2(S(S(y0)), z0)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z0), z1, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z0), z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z0, bot[7])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(y0, y1, y2)), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(y0, y1, y2)), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(y0, y1, y2)), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(y0, y1, y2)), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, y0), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, y0), z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), y3), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), y3), z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), y3), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), y3), z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(S(S(y2)), z1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), S(S(y2)), z1)) PLUS#2(S(S(S(y0))), z1) -> c5(PLUS#2(S(S(y0)), z1)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z0), z1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z0), z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z0, bot[7])) K tuples: ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x1, x2, x3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x1)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x1), x2, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x1, x2, x3), x4), x5, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x1, x2, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4), x5, bot[0]) -> c7(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4), x5, bot[0]) -> c7(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4), x5, bot[0]) -> c13(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4), x5, bot[0]) -> c13(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4), x5, bot[0]) -> c14(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4), x5, bot[0]) -> c14(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4), x5, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[0]) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x4)) Defined Rule Symbols: zipwith_l_f_xs_ys#1_4, cond_zipwith_l_f_xs_ys_2, cond_zipwith_l_f_xs_ys_1_3, fibs_2#1_4, zipwith_l#3_2, plus#2_2 Defined Pair Symbols: COND_TAKE_L_N_XS_2, COND_ZIPWITH_L_F_XS_YS_2, ZIPWITH_L_F_XS_YS#1_4, COND_ZIPWITH_L_F_XS_YS_1_3, PLUS#2_2 Compound Symbols: c3_2, c3_1, c8_2, c8_1, c10_1, c12_2, c_1, c1_1, c12_1, c4_1, c7_1, c13_1, c14_1, c11_1, c6_1, c2_1, c9_1, c5_1 ---------------------------------------- (155) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x1, x2, x3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x1, x2, x3))) by ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(y2, y3, y4)), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(y2, y3, y4)))) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, fibs, fibs_2(y2, y3, y4)), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(plus, fibs, fibs_2(y2, y3, y4)))) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, fibs, z2), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(plus, fibs, z2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, y2), z2), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, y2), z2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y2, y3, y4), y5), z2), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y2, y3, y4), y5), z2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y2, y3, y4), y5), z2), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y2, y3, y4), y5), z2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z2), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(y2, y3, y4)), z2), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(y2, y3, y4)), z2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(y2, y3, y4)), z2), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(y2, y3, y4)), z2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, y2), y3), z2), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, y2), y3), z2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y2, y3, y4), y5), y6), z2), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y2, y3, y4), y5), y6), z2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y2, y3, y4), y5), y6), z2), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y2, y3, y4), y5), y6), z2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), y2), z2), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), y2), z2))) ---------------------------------------- (156) Obligation: Complexity Dependency Tuples Problem Rules: zipwith_l_f_xs_ys#1(plus, fibs, z0, z1) -> cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0) zipwith_l_f_xs_ys#1(plus, fibs_2(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3) zipwith_l_f_xs_ys#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), zipwith_l_f_xs_ys(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), fibs_2(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys_1(ConsL(z0, z1), z2, z3) -> ConsL(plus#2(z2, z0), zipwith_l#3(z3, z1)) fibs_2#1(zipwith_l, plus, tail_l, z0) -> ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))) zipwith_l#3(z0, z1) -> zipwith_l_f_xs_ys(plus, z0, z1) plus#2(0, z0) -> z0 plus#2(S(z0), z1) -> S(plus#2(z0, z1)) Tuples: COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, x1)), S(x2)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, x2)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5, bot[6])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z1)), S(z2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z1), z2), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z1, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z2)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z2), z0, z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z2, bot[6])) ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x0)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x1), x2, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x0), x1, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x1, x2, x3), x4), x5, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x1, x2, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5), x6, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x0, x1, x2), x3), x4, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x0, x1, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4), x5, bot[0]) -> c7(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4), x5, bot[0]) -> c7(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4), x5, bot[0]) -> c13(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4), x5, bot[0]) -> c13(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4), x5, bot[0]) -> c14(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4), x5, bot[0]) -> c14(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4), x5, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5), x6, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[0]) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x4)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x5, bot[6]) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x5)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x0, bot[7]) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0)) COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), S(S(y0)), z3) -> c6(PLUS#2(S(S(y0)), z0)) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z4, bot[0])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z0), z1, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z0), z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z0, bot[7])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(y0, y1, y2)), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(y0, y1, y2)), z4, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(y0, y1, y2)), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(y0, y1, y2)), z4, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z3), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z3), z4, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z3), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z3), z4, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), z3), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), z3), z4, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, y0), z3), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, y0), z3), z4, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), y3), z3), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), y3), z3), z4, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), y3), z3), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), y3), z3), z4, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), z3), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), z3), z4, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(y0, y1, y2)), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(y0, y1, y2)), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(y0, y1, y2)), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(y0, y1, y2)), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, y0), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, y0), z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), y3), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), y3), z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), y3), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), y3), z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z4), z5, bot[6])) COND_TAKE_L_N_XS(ConsL(z0, fibs_2(zipwith_l, plus, tail_l)), S(S(y4))) -> c2(COND_TAKE_L_N_XS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), S(y4))) COND_ZIPWITH_L_F_XS_YS(ConsL(S(S(y2)), z1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), S(S(y2)), z1)) PLUS#2(S(S(S(y0))), z1) -> c5(PLUS#2(S(S(y0)), z1)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z0), z1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z0), z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z0), z1, bot[0]) -> c4(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z0), z1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(y2, y3, y4)), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(y2, y3, y4)))) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, fibs, fibs_2(y2, y3, y4)), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(plus, fibs, fibs_2(y2, y3, y4)))) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, fibs, z2), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(plus, fibs, z2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, y2), z2), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, y2), z2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y2, y3, y4), y5), z2), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y2, y3, y4), y5), z2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y2, y3, y4), y5), z2), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y2, y3, y4), y5), z2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z2), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(y2, y3, y4)), z2), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(y2, y3, y4)), z2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(y2, y3, y4)), z2), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(y2, y3, y4)), z2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, y2), y3), z2), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, y2), y3), z2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y2, y3, y4), y5), y6), z2), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y2, y3, y4), y5), y6), z2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y2, y3, y4), y5), y6), z2), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y2, y3, y4), y5), y6), z2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), y2), z2), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), y2), z2))) S tuples: COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, x2)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z2)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z2), z0, z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z2, bot[6])) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x0)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x0), x1, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5), x6, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x0, x1, x2), x3), x4, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x0, x1, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5), x6, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x5, bot[6]) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x5)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x0, bot[7]) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0)) COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), S(S(y0)), z3) -> c6(PLUS#2(S(S(y0)), z0)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z0), z1, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z0), z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z0, bot[7])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(y0, y1, y2)), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(y0, y1, y2)), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(y0, y1, y2)), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(y0, y1, y2)), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, y0), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, y0), z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), y3), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), y3), z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), y3), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), y3), z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(S(S(y2)), z1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), S(S(y2)), z1)) PLUS#2(S(S(S(y0))), z1) -> c5(PLUS#2(S(S(y0)), z1)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z0), z1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z0), z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z0, bot[7])) K tuples: ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x1)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x1), x2, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x1, x2, x3), x4), x5, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x1, x2, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4), x5, bot[0]) -> c7(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4), x5, bot[0]) -> c7(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4), x5, bot[0]) -> c13(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4), x5, bot[0]) -> c13(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4), x5, bot[0]) -> c14(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4), x5, bot[0]) -> c14(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4), x5, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[0]) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x4)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(y2, y3, y4)), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(y2, y3, y4)))) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, fibs, fibs_2(y2, y3, y4)), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(plus, fibs, fibs_2(y2, y3, y4)))) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, fibs, z2), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(plus, fibs, z2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, y2), z2), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, y2), z2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y2, y3, y4), y5), z2), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y2, y3, y4), y5), z2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y2, y3, y4), y5), z2), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y2, y3, y4), y5), z2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z2), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(y2, y3, y4)), z2), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(y2, y3, y4)), z2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(y2, y3, y4)), z2), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(y2, y3, y4)), z2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, y2), y3), z2), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, y2), y3), z2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y2, y3, y4), y5), y6), z2), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y2, y3, y4), y5), y6), z2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y2, y3, y4), y5), y6), z2), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y2, y3, y4), y5), y6), z2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), y2), z2), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), y2), z2))) Defined Rule Symbols: zipwith_l_f_xs_ys#1_4, cond_zipwith_l_f_xs_ys_2, cond_zipwith_l_f_xs_ys_1_3, fibs_2#1_4, zipwith_l#3_2, plus#2_2 Defined Pair Symbols: COND_TAKE_L_N_XS_2, COND_ZIPWITH_L_F_XS_YS_2, ZIPWITH_L_F_XS_YS#1_4, COND_ZIPWITH_L_F_XS_YS_1_3, PLUS#2_2 Compound Symbols: c3_2, c3_1, c8_2, c8_1, c10_1, c12_2, c_1, c1_1, c12_1, c4_1, c7_1, c13_1, c14_1, c11_1, c6_1, c2_1, c9_1, c5_1 ---------------------------------------- (157) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x1)) by ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(y2, y3, y4)), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(y2, y3, y4)))) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, fibs, fibs_2(y2, y3, y4)), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(plus, fibs, fibs_2(y2, y3, y4)))) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, fibs, y2), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(plus, fibs, y2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, y2), y3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, y2), y3))) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y2, y3, y4), y5), y6), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y2, y3, y4), y5), y6))) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y2, y3, y4), y5), y6), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y2, y3, y4), y5), y6))) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), y2), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), y2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(y2, y3, y4)), y5), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(y2, y3, y4)), y5))) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(y2, y3, y4)), y5), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(y2, y3, y4)), y5))) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, y2), y3), y4), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, y2), y3), y4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y2, y3, y4), y5), y6), y7), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y2, y3, y4), y5), y6), y7))) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y2, y3, y4), y5), y6), y7), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y2, y3, y4), y5), y6), y7))) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), y2), y3), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), y2), y3))) ---------------------------------------- (158) Obligation: Complexity Dependency Tuples Problem Rules: zipwith_l_f_xs_ys#1(plus, fibs, z0, z1) -> cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0) zipwith_l_f_xs_ys#1(plus, fibs_2(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3) zipwith_l_f_xs_ys#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), zipwith_l_f_xs_ys(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), fibs_2(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys_1(ConsL(z0, z1), z2, z3) -> ConsL(plus#2(z2, z0), zipwith_l#3(z3, z1)) fibs_2#1(zipwith_l, plus, tail_l, z0) -> ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))) zipwith_l#3(z0, z1) -> zipwith_l_f_xs_ys(plus, z0, z1) plus#2(0, z0) -> z0 plus#2(S(z0), z1) -> S(plus#2(z0, z1)) Tuples: COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, x1)), S(x2)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, x2)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5, bot[6])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z1)), S(z2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z1), z2), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z1, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z2)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z2), z0, z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z2, bot[6])) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x0)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x1), x2, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x0), x1, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x1, x2, x3), x4), x5, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x1, x2, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5), x6, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x0, x1, x2), x3), x4, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x0, x1, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4), x5, bot[0]) -> c7(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4), x5, bot[0]) -> c7(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4), x5, bot[0]) -> c13(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4), x5, bot[0]) -> c13(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4), x5, bot[0]) -> c14(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4), x5, bot[0]) -> c14(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4), x5, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5), x6, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[0]) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x4)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x5, bot[6]) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x5)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x0, bot[7]) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0)) COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), S(S(y0)), z3) -> c6(PLUS#2(S(S(y0)), z0)) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z4, bot[0])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z0), z1, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z0), z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z0, bot[7])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(y0, y1, y2)), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(y0, y1, y2)), z4, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(y0, y1, y2)), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(y0, y1, y2)), z4, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z3), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z3), z4, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z3), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z3), z4, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), z3), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), z3), z4, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, y0), z3), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, y0), z3), z4, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), y3), z3), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), y3), z3), z4, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), y3), z3), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), y3), z3), z4, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), z3), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), z3), z4, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(y0, y1, y2)), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(y0, y1, y2)), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(y0, y1, y2)), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(y0, y1, y2)), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, y0), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, y0), z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), y3), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), y3), z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), y3), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), y3), z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z4), z5, bot[6])) COND_TAKE_L_N_XS(ConsL(z0, fibs_2(zipwith_l, plus, tail_l)), S(S(y4))) -> c2(COND_TAKE_L_N_XS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), S(y4))) COND_ZIPWITH_L_F_XS_YS(ConsL(S(S(y2)), z1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), S(S(y2)), z1)) PLUS#2(S(S(S(y0))), z1) -> c5(PLUS#2(S(S(y0)), z1)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z0), z1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z0), z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z0), z1, bot[0]) -> c4(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z0), z1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(y2, y3, y4)), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(y2, y3, y4)))) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, fibs, fibs_2(y2, y3, y4)), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(plus, fibs, fibs_2(y2, y3, y4)))) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, fibs, z2), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(plus, fibs, z2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, y2), z2), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, y2), z2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y2, y3, y4), y5), z2), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y2, y3, y4), y5), z2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y2, y3, y4), y5), z2), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y2, y3, y4), y5), z2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z2), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(y2, y3, y4)), z2), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(y2, y3, y4)), z2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(y2, y3, y4)), z2), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(y2, y3, y4)), z2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, y2), y3), z2), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, y2), y3), z2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y2, y3, y4), y5), y6), z2), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y2, y3, y4), y5), y6), z2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y2, y3, y4), y5), y6), z2), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y2, y3, y4), y5), y6), z2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), y2), z2), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), y2), z2))) S tuples: COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, x2)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z2)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z2), z0, z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z2, bot[6])) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x0)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x0), x1, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5), x6, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x0, x1, x2), x3), x4, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x0, x1, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5), x6, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x5, bot[6]) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x5)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x0, bot[7]) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0)) COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), S(S(y0)), z3) -> c6(PLUS#2(S(S(y0)), z0)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z0), z1, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z0), z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z0, bot[7])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(y0, y1, y2)), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(y0, y1, y2)), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(y0, y1, y2)), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(y0, y1, y2)), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, y0), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, y0), z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), y3), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), y3), z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), y3), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), y3), z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(S(S(y2)), z1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), S(S(y2)), z1)) PLUS#2(S(S(S(y0))), z1) -> c5(PLUS#2(S(S(y0)), z1)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z0), z1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z0), z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z0, bot[7])) K tuples: ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x1), x2, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x1, x2, x3), x4), x5, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x1, x2, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4), x5, bot[0]) -> c7(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4), x5, bot[0]) -> c7(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4), x5, bot[0]) -> c13(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4), x5, bot[0]) -> c13(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4), x5, bot[0]) -> c14(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4), x5, bot[0]) -> c14(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4), x5, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[0]) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x4)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(y2, y3, y4)), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(y2, y3, y4)))) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, fibs, fibs_2(y2, y3, y4)), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(plus, fibs, fibs_2(y2, y3, y4)))) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, fibs, z2), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(plus, fibs, z2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, y2), z2), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, y2), z2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y2, y3, y4), y5), z2), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y2, y3, y4), y5), z2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y2, y3, y4), y5), z2), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y2, y3, y4), y5), z2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z2), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(y2, y3, y4)), z2), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(y2, y3, y4)), z2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(y2, y3, y4)), z2), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(y2, y3, y4)), z2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, y2), y3), z2), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, y2), y3), z2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y2, y3, y4), y5), y6), z2), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y2, y3, y4), y5), y6), z2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y2, y3, y4), y5), y6), z2), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y2, y3, y4), y5), y6), z2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), y2), z2), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), y2), z2))) Defined Rule Symbols: zipwith_l_f_xs_ys#1_4, cond_zipwith_l_f_xs_ys_2, cond_zipwith_l_f_xs_ys_1_3, fibs_2#1_4, zipwith_l#3_2, plus#2_2 Defined Pair Symbols: COND_TAKE_L_N_XS_2, COND_ZIPWITH_L_F_XS_YS_2, ZIPWITH_L_F_XS_YS#1_4, COND_ZIPWITH_L_F_XS_YS_1_3, PLUS#2_2 Compound Symbols: c3_2, c3_1, c8_2, c8_1, c10_1, c12_2, c_1, c1_1, c12_1, c4_1, c7_1, c13_1, c14_1, c11_1, c6_1, c2_1, c9_1, c5_1 ---------------------------------------- (159) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (160) Obligation: Complexity Dependency Tuples Problem Rules: zipwith_l_f_xs_ys#1(plus, fibs, z0, z1) -> cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0) zipwith_l_f_xs_ys#1(plus, fibs_2(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3) zipwith_l_f_xs_ys#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), zipwith_l_f_xs_ys(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys(ConsL(z0, z1), fibs_2(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), z0, z1) cond_zipwith_l_f_xs_ys_1(ConsL(z0, z1), z2, z3) -> ConsL(plus#2(z2, z0), zipwith_l#3(z3, z1)) fibs_2#1(zipwith_l, plus, tail_l, z0) -> ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))) zipwith_l#3(z0, z1) -> zipwith_l_f_xs_ys(plus, z0, z1) plus#2(0, z0) -> z0 plus#2(S(z0), z1) -> S(plus#2(z0, z1)) Tuples: COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, x1)), S(x2)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x4, bot[0])) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4)), S(x5)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x4), x5), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x4, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, x2)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5, bot[6])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z1)), S(z2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z1), z2), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z1, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z2)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z2), z0, z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z2, bot[6])) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x0)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x1), x2, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x0), x1, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x1, x2, x3), x4), x5, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x1, x2, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5), x6, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x0, x1, x2), x3), x4, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x0, x1, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4), x5, bot[0]) -> c7(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4), x5, bot[0]) -> c7(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4), x5, bot[0]) -> c13(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4), x5, bot[0]) -> c13(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4), x5, bot[0]) -> c14(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4), x5, bot[0]) -> c14(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4), x5, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5), x6, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[0]) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x4)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x5, bot[6]) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x5)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x0, bot[7]) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0)) COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), S(S(y0)), z3) -> c6(PLUS#2(S(S(y0)), z0)) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z4, bot[0])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z0), z1, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z0), z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z0, bot[7])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(y0, y1, y2)), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(y0, y1, y2)), z4, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(y0, y1, y2)), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(y0, y1, y2)), z4, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z3), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z3), z4, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z3), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z3), z4, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), z3), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), z3), z4, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, y0), z3), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, y0), z3), z4, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), y3), z3), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), y3), z3), z4, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), y3), z3), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), y3), z3), z4, bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), z3), z4)), S(z5)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), z3), z4, bot[0])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(y0, y1, y2)), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(y0, y1, y2)), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(y0, y1, y2)), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(y0, y1, y2)), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, y0), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, y0), z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), y3), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), y3), z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), y3), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), y3), z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z4), z5, bot[6])) COND_TAKE_L_N_XS(ConsL(z0, fibs_2(zipwith_l, plus, tail_l)), S(S(y4))) -> c2(COND_TAKE_L_N_XS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), S(y4))) COND_ZIPWITH_L_F_XS_YS(ConsL(S(S(y2)), z1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), S(S(y2)), z1)) PLUS#2(S(S(S(y0))), z1) -> c5(PLUS#2(S(S(y0)), z1)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z0), z1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z0), z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z0), z1, bot[0]) -> c4(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z0), z1)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(y2, y3, y4)), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(y2, y3, y4)))) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, fibs, fibs_2(y2, y3, y4)), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(plus, fibs, fibs_2(y2, y3, y4)))) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, fibs, z2), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(plus, fibs, z2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, y2), z2), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, y2), z2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y2, y3, y4), y5), z2), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y2, y3, y4), y5), z2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y2, y3, y4), y5), z2), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y2, y3, y4), y5), z2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z2), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(y2, y3, y4)), z2), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(y2, y3, y4)), z2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(y2, y3, y4)), z2), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(y2, y3, y4)), z2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, y2), y3), z2), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, y2), y3), z2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y2, y3, y4), y5), y6), z2), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y2, y3, y4), y5), y6), z2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y2, y3, y4), y5), y6), z2), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y2, y3, y4), y5), y6), z2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), y2), z2), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), y2), z2))) COND_TAKE_L_N_XS(ConsL(x0, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))), S(x2)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) S tuples: COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, fibs_2(z2, z3, z4))) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z2, z3, z4), bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, fibs, x2)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z0), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z0), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(x0, x1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), z3), x5), x0, x1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3), x5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z2)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z2), z0, z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z2, bot[6])) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x2, x3, x4), bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x2, x3, x4))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[6]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(x0, x1, x2), bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(x0, x1, x2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x0)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x3, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x3), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x1), ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x2, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x0), x1, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x0, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x2, x3, x4), x5), x6, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x2, x3, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x0, x1, x2), x3), x4, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x0, x1, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x4), x5), x6, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x4), x5), x6), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3), x4, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x2), x3), x4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5), x6, bot[6]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x2, x3, x4), x5, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2), x3, bot[7]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), x2, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x5, bot[6]) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x5)) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x0, bot[7]) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x0)) COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), S(S(y0)), z3) -> c6(PLUS#2(S(S(y0)), z0)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z0), z1, bot[6]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z0), z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z0, bot[7])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(y0, y1, y2)), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(y0, y1, y2)), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(y0, y1, y2)), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(y0, y1, y2)), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, y0), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, y0), z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), y3), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), y3), z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), y3), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), y3), z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z4), z5)) -> c8(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z4), z5, bot[6])) COND_ZIPWITH_L_F_XS_YS(ConsL(S(S(y2)), z1), fibs_2(zipwith_l, plus, tail_l)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), S(S(y2)), z1)) PLUS#2(S(S(S(y0))), z1) -> c5(PLUS#2(S(S(y0)), z1)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z0), z1, bot[7]) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), z0), z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z0, bot[7])) K tuples: ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2)), x2, bot[0]) -> c(ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys_1(fibs_2#1(z0, z1, z2, bot[6]), 0, fibs_2(zipwith_l, plus, tail_l)), x2)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(z0, z1, z2)), x2, bot[0]) -> c1(ZIPWITH_L_F_XS_YS#1(plus, fibs, fibs_2(z0, z1, z2), bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x1), x2, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs, x1, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), x4), x5, bot[0]) -> c4(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(x1, x2, x3), x4), x5, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, fibs_2(x1, x2, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4), x5, bot[0]) -> c7(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4), x5, bot[0]) -> c7(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4), x5, bot[0]) -> c13(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, bot[7]), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4), x5, bot[0]) -> c13(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z0, z1, z2), x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4), x5, bot[0]) -> c14(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, bot[7]), x3), x4), x5)) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4), x5, bot[0]) -> c14(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0, z1, z2), x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4), x5, bot[0]) -> c12(ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(x1, x2, x3), x4, bot[7])) ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), x4, bot[0]) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l_f_xs_ys(plus, fibs, fibs_2(zipwith_l, plus, tail_l))), x4)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(y2, y3, y4)), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(y2, y3, y4)))) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, fibs, fibs_2(y2, y3, y4)), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(plus, fibs, fibs_2(y2, y3, y4)))) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, fibs, z2), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(plus, fibs, z2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, y2), z2), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, y2), z2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y2, y3, y4), y5), z2), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y2, y3, y4), y5), z2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y2, y3, y4), y5), z2), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y2, y3, y4), y5), z2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z2), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), z2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(y2, y3, y4)), z2), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(y2, y3, y4)), z2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(y2, y3, y4)), z2), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(y2, y3, y4)), z2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, y2), y3), z2), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, y2), y3), z2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y2, y3, y4), y5), y6), z2), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y2, y3, y4), y5), y6), z2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y2, y3, y4), y5), y6), z2), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y2, y3, y4), y5), y6), z2))) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), y2), z2), bot[0]) -> c10(COND_ZIPWITH_L_F_XS_YS(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), y2), z2))) Defined Rule Symbols: zipwith_l_f_xs_ys#1_4, cond_zipwith_l_f_xs_ys_2, cond_zipwith_l_f_xs_ys_1_3, fibs_2#1_4, zipwith_l#3_2, plus#2_2 Defined Pair Symbols: COND_TAKE_L_N_XS_2, COND_ZIPWITH_L_F_XS_YS_2, ZIPWITH_L_F_XS_YS#1_4, COND_ZIPWITH_L_F_XS_YS_1_3, PLUS#2_2 Compound Symbols: c3_2, c3_1, c8_2, c8_1, c10_1, c12_2, c_1, c1_1, c12_1, c4_1, c7_1, c13_1, c14_1, c11_1, c6_1, c2_1, c9_1, c5_1