KILLED proof of input_NQ1d5XHVXV.trs # AProVE Commit ID: 5b976082cb74a395683ed8cc7acf94bd611ab29f fuhs 20230524 unpublished The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF). (0) CpxTRS (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxTRS (3) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (4) CpxTRS (5) CpxTrsToCdtProof [BOTH BOUNDS(ID, ID), 0 ms] (6) CdtProblem (7) CdtToCpxRelTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (8) CpxRelTRS (9) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (10) CpxRelTRS (11) TypeInferenceProof [BOTH BOUNDS(ID, ID), 9 ms] (12) typed CpxTrs (13) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 2 ms] (14) TRS for Loop Detection (15) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] (16) CdtProblem (17) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms] (18) CdtProblem (19) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (20) CdtProblem (21) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms] (22) CdtProblem (23) CdtToCpxRelTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (24) CpxRelTRS (25) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (26) CpxTRS (27) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (28) CpxWeightedTrs (29) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (30) CpxTypedWeightedTrs (31) CompletionProof [UPPER BOUND(ID), 0 ms] (32) CpxTypedWeightedCompleteTrs (33) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (34) CpxTypedWeightedCompleteTrs (35) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (36) CpxRNTS (37) InliningProof [UPPER BOUND(ID), 597 ms] (38) CpxRNTS (39) SimplificationProof [BOTH BOUNDS(ID, ID), 13 ms] (40) CpxRNTS (41) CompletionProof [UPPER BOUND(ID), 0 ms] (42) CpxTypedWeightedCompleteTrs (43) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (44) CpxRNTS (45) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 194 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), 0 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) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (70) CdtProblem (71) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (72) CdtProblem (73) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (74) CdtProblem (75) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (76) CdtProblem (77) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (78) CdtProblem (79) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (80) CdtProblem (81) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (82) CdtProblem (83) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms] (84) CdtProblem (85) CdtInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (86) CdtProblem (87) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 106 ms] (88) CdtProblem (89) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms] (90) CdtProblem (91) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (92) CdtProblem (93) CdtInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (94) CdtProblem (95) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms] (96) CdtProblem (97) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 125 ms] (98) CdtProblem (99) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (100) CdtProblem (101) CdtInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (102) CdtProblem (103) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms] (104) CdtProblem (105) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 164 ms] (106) CdtProblem (107) CdtInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (108) CdtProblem (109) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 152 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)), 129 ms] (116) CdtProblem (117) CdtInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (118) CdtProblem (119) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 161 ms] (120) CdtProblem (121) CdtInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (122) CdtProblem (123) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms] (124) CdtProblem (125) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 143 ms] (126) CdtProblem (127) CdtInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (128) CdtProblem (129) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms] (130) CdtProblem (131) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 151 ms] (132) CdtProblem (133) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (134) CdtProblem (135) CdtInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (136) CdtProblem (137) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms] (138) CdtProblem (139) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 212 ms] (140) CdtProblem (141) CdtInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (142) CdtProblem (143) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 195 ms] (144) CdtProblem (145) CdtInstantiationProof [BOTH BOUNDS(ID, ID), 1 ms] (146) CdtProblem (147) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 207 ms] (148) CdtProblem (149) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (150) CdtProblem (151) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 3 ms] (152) CdtProblem (153) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 16 ms] (154) CdtProblem (155) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (156) CdtProblem (157) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (158) CdtProblem (159) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (160) CdtProblem (161) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (162) CdtProblem (163) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 9 ms] (164) CdtProblem (165) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (166) CdtProblem (167) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (168) CdtProblem (169) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (170) CdtProblem (171) CdtRewritingProof [BOTH BOUNDS(ID, ID), 12 ms] (172) CdtProblem (173) RelTrsToWeightedTrsProof [UPPER BOUND(ID), 0 ms] (174) CpxWeightedTrs (175) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (176) CpxTypedWeightedTrs (177) CompletionProof [UPPER BOUND(ID), 0 ms] (178) CpxTypedWeightedCompleteTrs (179) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (180) CpxTypedWeightedCompleteTrs (181) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 1 ms] (182) CpxRNTS (183) InliningProof [UPPER BOUND(ID), 266 ms] (184) CpxRNTS (185) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] (186) CpxRNTS (187) CompletionProof [UPPER BOUND(ID), 0 ms] (188) CpxTypedWeightedCompleteTrs (189) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 9 ms] (190) CpxRNTS ---------------------------------------- (0) Obligation: The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: 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) CpxTrsToCdtProof (BOTH BOUNDS(ID, ID)) Converted Cpx (relative) TRS with rewrite strategy PARALLEL_INNERMOST to CDT ---------------------------------------- (6) 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 ---------------------------------------- (7) CdtToCpxRelTrsProof (BOTH BOUNDS(ID, ID)) Converted S to standard rules, and D \ S as well as R to relative rules. ---------------------------------------- (8) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: 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)) The (relative) TRS S consists of the following 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) Rewrite Strategy: INNERMOST ---------------------------------------- (9) RenamingProof (BOTH BOUNDS(ID, ID)) Renamed function symbols to avoid clashes with predefined symbol. ---------------------------------------- (10) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: 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)) The (relative) TRS S consists of the following 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) Rewrite Strategy: INNERMOST ---------------------------------------- (11) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Inferred types. ---------------------------------------- (12) Obligation: Innermost TRS: Rules: 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)) 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) Types: FIBS_2#1 :: zipwith_l -> plus -> tail_l -> bot[0]:bot[6]:bot[7] -> c zipwith_l :: zipwith_l plus :: plus tail_l :: tail_l c :: c13 -> c ZIPWITH_L#3 :: fibs:fibs_2:zipwith_l_f_xs_ys -> fibs:fibs_2:zipwith_l_f_xs_ys -> c13 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 -> c1:c2:c3 ConsL :: 0':S -> fibs:fibs_2:zipwith_l_f_xs_ys -> ConsL 0' :: 0':S c1 :: c1:c2:c3 S :: 0':S -> 0':S c2 :: c1:c2:c3 -> c -> c1:c2:c3 fibs_2#1 :: zipwith_l -> plus -> tail_l -> bot[0]:bot[6]:bot[7] -> ConsL 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 c3 :: c1:c2:c3 -> c10:c11:c12 -> c1:c2:c3 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 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] -> c10:c11:c12 PLUS#2 :: 0':S -> 0':S -> c4:c5 c4 :: c4:c5 c5 :: c4:c5 -> c4:c5 COND_ZIPWITH_L_F_XS_YS_1 :: ConsL -> 0':S -> fibs:fibs_2:zipwith_l_f_xs_ys -> c6:c7 c6 :: c4:c5 -> c6:c7 c7 :: c13 -> c6:c7 COND_ZIPWITH_L_F_XS_YS :: ConsL -> fibs:fibs_2:zipwith_l_f_xs_ys -> c8:c9 c8 :: c6:c7 -> c10:c11:c12 -> c8:c9 bot[6] :: bot[0]:bot[6]:bot[7] c9 :: c6:c7 -> c -> c8:c9 c10 :: c8:c9 -> c10:c11:c12 c11 :: c8:c9 -> c -> c10:c11:c12 bot[7] :: bot[0]:bot[6]:bot[7] c12 :: c8:c9 -> c10:c11:c12 -> c10:c11:c12 c13 :: c13 MAIN :: 0':S -> c14 c14 :: c1:c2:c3 -> c14 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 cond_take_l_n_xs :: ConsL -> 0':S -> Nil:Cons Nil :: Nil:Cons Cons :: 0':S -> Nil:Cons -> Nil:Cons 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 main :: 0':S -> Nil:Cons hole_c1_15 :: c hole_zipwith_l2_15 :: zipwith_l hole_plus3_15 :: plus hole_tail_l4_15 :: tail_l hole_bot[0]:bot[6]:bot[7]5_15 :: bot[0]:bot[6]:bot[7] hole_c136_15 :: c13 hole_fibs:fibs_2:zipwith_l_f_xs_ys7_15 :: fibs:fibs_2:zipwith_l_f_xs_ys hole_c1:c2:c38_15 :: c1:c2:c3 hole_ConsL9_15 :: ConsL hole_0':S10_15 :: 0':S hole_c10:c11:c1211_15 :: c10:c11:c12 hole_c4:c512_15 :: c4:c5 hole_c6:c713_15 :: c6:c7 hole_c8:c914_15 :: c8:c9 hole_c1415_15 :: c14 hole_Nil:Cons16_15 :: Nil:Cons gen_fibs:fibs_2:zipwith_l_f_xs_ys17_15 :: Nat -> fibs:fibs_2:zipwith_l_f_xs_ys gen_c1:c2:c318_15 :: Nat -> c1:c2:c3 gen_0':S19_15 :: Nat -> 0':S gen_c10:c11:c1220_15 :: Nat -> c10:c11:c12 gen_c4:c521_15 :: Nat -> c4:c5 gen_Nil:Cons22_15 :: Nat -> Nil:Cons ---------------------------------------- (13) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) Transformed a relative TRS into a decreasing-loop problem. ---------------------------------------- (14) Obligation: Analyzing the following TRS for decreasing loops: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: 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)) The (relative) TRS S consists of the following 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) Rewrite Strategy: INNERMOST ---------------------------------------- (15) CpxTrsToCdtProof (UPPER BOUND(ID)) Converted Cpx (relative) TRS with rewrite strategy PARALLEL_INNERMOST to CDT ---------------------------------------- (16) 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 ---------------------------------------- (17) 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: FIBS_2#1(zipwith_l, plus, tail_l, z0) -> c(ZIPWITH_L#3(fibs, fibs_2(zipwith_l, plus, tail_l))) COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c7(ZIPWITH_L#3(z3, z1)) ZIPWITH_L#3(z0, z1) -> c13 PLUS#2(0, z0) -> c4 COND_TAKE_L_N_XS(ConsL(z0, z1), 0) -> c1 ---------------------------------------- (18) 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 ---------------------------------------- (19) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (20) 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 ---------------------------------------- (21) 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) ---------------------------------------- (22) 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 ---------------------------------------- (23) CdtToCpxRelTrsProof (BOTH BOUNDS(ID, ID)) Converted S to standard rules, and D \ S as well as R to relative rules. ---------------------------------------- (24) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: 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 (relative) TRS S consists of the following 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)) Rewrite Strategy: INNERMOST ---------------------------------------- (25) RelTrsToTrsProof (UPPER BOUND(ID)) transformed relative TRS to TRS ---------------------------------------- (26) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: 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)) 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)) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (27) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) Transformed relative TRS to weighted TRS ---------------------------------------- (28) 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: 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])) [1] PLUS#2(S(z0), z1) -> c5(PLUS#2(z0, z1)) [1] COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) [1] 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])) [1] 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)) [1] 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])) [1] 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)) [1] 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)) [1] 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)) [1] 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) [0] 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) [0] 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) [0] 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) [0] 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) [0] cond_zipwith_l_f_xs_ys_1(ConsL(z0, z1), z2, z3) -> ConsL(plus#2(z2, z0), zipwith_l#3(z3, z1)) [0] fibs_2#1(zipwith_l, plus, tail_l, z0) -> ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))) [0] zipwith_l#3(z0, z1) -> zipwith_l_f_xs_ys(plus, z0, z1) [0] plus#2(0, z0) -> z0 [0] plus#2(S(z0), z1) -> S(plus#2(z0, z1)) [0] Rewrite Strategy: INNERMOST ---------------------------------------- (29) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (30) Obligation: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: 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])) [1] PLUS#2(S(z0), z1) -> c5(PLUS#2(z0, z1)) [1] COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) [1] 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])) [1] 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)) [1] 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])) [1] 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)) [1] 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)) [1] 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)) [1] 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) [0] 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) [0] 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) [0] 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) [0] 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) [0] cond_zipwith_l_f_xs_ys_1(ConsL(z0, z1), z2, z3) -> ConsL(plus#2(z2, z0), zipwith_l#3(z3, z1)) [0] fibs_2#1(zipwith_l, plus, tail_l, z0) -> ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))) [0] zipwith_l#3(z0, z1) -> zipwith_l_f_xs_ys(plus, z0, z1) [0] plus#2(0, z0) -> z0 [0] plus#2(S(z0), z1) -> S(plus#2(z0, z1)) [0] The TRS has the following type information: COND_TAKE_L_N_XS :: ConsL -> S:0 -> c3:c2 ConsL :: S:0 -> zipwith_l_f_xs_ys:fibs:fibs_2 -> ConsL zipwith_l_f_xs_ys :: plus -> zipwith_l_f_xs_ys:fibs:fibs_2 -> zipwith_l_f_xs_ys:fibs:fibs_2 -> zipwith_l_f_xs_ys:fibs:fibs_2 S :: S:0 -> S:0 c3 :: c3:c2 -> c10:c12:c11 -> c3:c2 zipwith_l_f_xs_ys#1 :: plus -> zipwith_l_f_xs_ys:fibs:fibs_2 -> zipwith_l_f_xs_ys:fibs:fibs_2 -> bot[0]:bot[6]:bot[7] -> ConsL bot[0] :: bot[0]:bot[6]:bot[7] ZIPWITH_L_F_XS_YS#1 :: plus -> zipwith_l_f_xs_ys:fibs:fibs_2 -> zipwith_l_f_xs_ys:fibs:fibs_2 -> bot[0]:bot[6]:bot[7] -> c10:c12:c11 PLUS#2 :: S:0 -> S:0 -> c5 c5 :: c5 -> c5 COND_ZIPWITH_L_F_XS_YS_1 :: ConsL -> S:0 -> zipwith_l_f_xs_ys:fibs:fibs_2 -> c6 c6 :: c5 -> c6 COND_ZIPWITH_L_F_XS_YS :: ConsL -> zipwith_l_f_xs_ys:fibs:fibs_2 -> c8:c9 c8 :: c6 -> c10:c12:c11 -> c8:c9 bot[6] :: bot[0]:bot[6]:bot[7] plus :: plus fibs :: zipwith_l_f_xs_ys:fibs:fibs_2 c10 :: c8:c9 -> c10:c12:c11 0 :: S:0 fibs_2 :: zipwith_l -> plus -> tail_l -> zipwith_l_f_xs_ys:fibs:fibs_2 zipwith_l :: zipwith_l tail_l :: tail_l c12 :: c8:c9 -> c10:c12:c11 -> c10:c12:c11 bot[7] :: bot[0]:bot[6]:bot[7] c2 :: c3:c2 -> c3:c2 fibs_2#1 :: zipwith_l -> plus -> tail_l -> bot[0]:bot[6]:bot[7] -> ConsL c9 :: c6 -> c8:c9 c11 :: c8:c9 -> c10:c12:c11 cond_zipwith_l_f_xs_ys :: ConsL -> zipwith_l_f_xs_ys:fibs:fibs_2 -> ConsL cond_zipwith_l_f_xs_ys_1 :: ConsL -> S:0 -> zipwith_l_f_xs_ys:fibs:fibs_2 -> ConsL plus#2 :: S:0 -> S:0 -> S:0 zipwith_l#3 :: zipwith_l_f_xs_ys:fibs:fibs_2 -> zipwith_l_f_xs_ys:fibs:fibs_2 -> zipwith_l_f_xs_ys:fibs:fibs_2 Rewrite Strategy: INNERMOST ---------------------------------------- (31) 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 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 (c) The following functions are completely defined: 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 Due to the following rules being added: zipwith_l_f_xs_ys#1(v0, v1, v2, v3) -> const1 [0] cond_zipwith_l_f_xs_ys(v0, v1) -> const1 [0] cond_zipwith_l_f_xs_ys_1(v0, v1, v2) -> const1 [0] fibs_2#1(v0, v1, v2, v3) -> const1 [0] zipwith_l#3(v0, v1) -> fibs [0] plus#2(v0, v1) -> 0 [0] And the following fresh constants: const1, const, const2, const3, const4, const5 ---------------------------------------- (32) 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: 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])) [1] PLUS#2(S(z0), z1) -> c5(PLUS#2(z0, z1)) [1] COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) [1] 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])) [1] 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)) [1] 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])) [1] 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)) [1] 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)) [1] 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)) [1] 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) [0] 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) [0] 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) [0] 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) [0] 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) [0] cond_zipwith_l_f_xs_ys_1(ConsL(z0, z1), z2, z3) -> ConsL(plus#2(z2, z0), zipwith_l#3(z3, z1)) [0] fibs_2#1(zipwith_l, plus, tail_l, z0) -> ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))) [0] zipwith_l#3(z0, z1) -> zipwith_l_f_xs_ys(plus, z0, z1) [0] plus#2(0, z0) -> z0 [0] plus#2(S(z0), z1) -> S(plus#2(z0, z1)) [0] zipwith_l_f_xs_ys#1(v0, v1, v2, v3) -> const1 [0] cond_zipwith_l_f_xs_ys(v0, v1) -> const1 [0] cond_zipwith_l_f_xs_ys_1(v0, v1, v2) -> const1 [0] fibs_2#1(v0, v1, v2, v3) -> const1 [0] zipwith_l#3(v0, v1) -> fibs [0] plus#2(v0, v1) -> 0 [0] The TRS has the following type information: COND_TAKE_L_N_XS :: ConsL:const1 -> S:0 -> c3:c2 ConsL :: S:0 -> zipwith_l_f_xs_ys:fibs:fibs_2 -> ConsL:const1 zipwith_l_f_xs_ys :: plus -> zipwith_l_f_xs_ys:fibs:fibs_2 -> zipwith_l_f_xs_ys:fibs:fibs_2 -> zipwith_l_f_xs_ys:fibs:fibs_2 S :: S:0 -> S:0 c3 :: c3:c2 -> c10:c12:c11 -> c3:c2 zipwith_l_f_xs_ys#1 :: plus -> zipwith_l_f_xs_ys:fibs:fibs_2 -> zipwith_l_f_xs_ys:fibs:fibs_2 -> bot[0]:bot[6]:bot[7] -> ConsL:const1 bot[0] :: bot[0]:bot[6]:bot[7] ZIPWITH_L_F_XS_YS#1 :: plus -> zipwith_l_f_xs_ys:fibs:fibs_2 -> zipwith_l_f_xs_ys:fibs:fibs_2 -> bot[0]:bot[6]:bot[7] -> c10:c12:c11 PLUS#2 :: S:0 -> S:0 -> c5 c5 :: c5 -> c5 COND_ZIPWITH_L_F_XS_YS_1 :: ConsL:const1 -> S:0 -> zipwith_l_f_xs_ys:fibs:fibs_2 -> c6 c6 :: c5 -> c6 COND_ZIPWITH_L_F_XS_YS :: ConsL:const1 -> zipwith_l_f_xs_ys:fibs:fibs_2 -> c8:c9 c8 :: c6 -> c10:c12:c11 -> c8:c9 bot[6] :: bot[0]:bot[6]:bot[7] plus :: plus fibs :: zipwith_l_f_xs_ys:fibs:fibs_2 c10 :: c8:c9 -> c10:c12:c11 0 :: S:0 fibs_2 :: zipwith_l -> plus -> tail_l -> zipwith_l_f_xs_ys:fibs:fibs_2 zipwith_l :: zipwith_l tail_l :: tail_l c12 :: c8:c9 -> c10:c12:c11 -> c10:c12:c11 bot[7] :: bot[0]:bot[6]:bot[7] c2 :: c3:c2 -> c3:c2 fibs_2#1 :: zipwith_l -> plus -> tail_l -> bot[0]:bot[6]:bot[7] -> ConsL:const1 c9 :: c6 -> c8:c9 c11 :: c8:c9 -> c10:c12:c11 cond_zipwith_l_f_xs_ys :: ConsL:const1 -> zipwith_l_f_xs_ys:fibs:fibs_2 -> ConsL:const1 cond_zipwith_l_f_xs_ys_1 :: ConsL:const1 -> S:0 -> zipwith_l_f_xs_ys:fibs:fibs_2 -> ConsL:const1 plus#2 :: S:0 -> S:0 -> S:0 zipwith_l#3 :: zipwith_l_f_xs_ys:fibs:fibs_2 -> zipwith_l_f_xs_ys:fibs:fibs_2 -> zipwith_l_f_xs_ys:fibs:fibs_2 const1 :: ConsL:const1 const :: c3:c2 const2 :: c10:c12:c11 const3 :: c5 const4 :: c6 const5 :: c8:c9 Rewrite Strategy: INNERMOST ---------------------------------------- (33) NarrowingProof (BOTH BOUNDS(ID, ID)) Narrowed the inner basic terms of all right-hand sides by a single narrowing step. ---------------------------------------- (34) 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: COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, fibs, z3)), S(z4)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z3), z4), ZIPWITH_L_F_XS_YS#1(plus, fibs, z3, bot[0])) [1] COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, fibs_2(z0', z1', z2'), z3)), S(z4)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(fibs_2#1(z0', z1', z2', bot[7]), z3), z4), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(z0', z1', z2'), z3, bot[0])) [1] COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z0'', z1'', z2''), z3)), S(z4)) -> c3(COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0'', z1'', z2'', bot[7]), z3), z4), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(z0'', z1'', z2''), z3, bot[0])) [1] COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(z1, z2, z3)), S(z4)) -> c3(COND_TAKE_L_N_XS(const1, z4), ZIPWITH_L_F_XS_YS#1(z1, z2, z3, bot[0])) [1] PLUS#2(S(z0), z1) -> c5(PLUS#2(z0, z1)) [1] COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) [1] COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs, z4)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z4), z0, z1), ZIPWITH_L_F_XS_YS#1(plus, fibs, z4, bot[6])) [1] COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(z01, z11, z21), z4)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(fibs_2#1(z01, z11, z21, bot[7]), z4), z0, z1), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(z01, z11, z21), z4, bot[6])) [1] COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z02, z12, z22), z4)) -> c8(COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z02, z12, z22, bot[7]), z4), z0, z1), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(z02, z12, z22), z4, bot[6])) [1] 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(const1, z0, z1), ZIPWITH_L_F_XS_YS#1(z2, z3, z4, bot[6])) [1] 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)) [1] ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs, z2), z3, z4) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z2), z3), ZIPWITH_L_F_XS_YS#1(plus, fibs, z2, bot[7])) [1] ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z03, z13, z23), z2), z3, z4) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(fibs_2#1(z03, z13, z23, bot[7]), z2), z3), ZIPWITH_L_F_XS_YS#1(plus, fibs_2(z03, z13, z23), z2, bot[7])) [1] ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z04, z14, z24), z2), z3, z4) -> c12(COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z04, z14, z24, bot[7]), z2), z3), ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(z04, z14, z24), z2, bot[7])) [1] ZIPWITH_L_F_XS_YS#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, z4) -> c12(COND_ZIPWITH_L_F_XS_YS(const1, z3), ZIPWITH_L_F_XS_YS#1(z0, z1, z2, bot[7])) [1] COND_TAKE_L_N_XS(ConsL(z0, fibs_2(zipwith_l, plus, tail_l)), S(z4)) -> c2(COND_TAKE_L_N_XS(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), z4)) [1] COND_TAKE_L_N_XS(ConsL(z0, fibs_2(z1, z2, z3)), S(z4)) -> c2(COND_TAKE_L_N_XS(const1, z4)) [1] COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), 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))), z0, z1)) [1] COND_ZIPWITH_L_F_XS_YS(ConsL(z0, z1), fibs_2(z2, z3, z4)) -> c9(COND_ZIPWITH_L_F_XS_YS_1(const1, z0, z1)) [1] ZIPWITH_L_F_XS_YS#1(plus, fibs_2(zipwith_l, plus, tail_l), z3, z4) -> c11(COND_ZIPWITH_L_F_XS_YS(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), z3)) [1] ZIPWITH_L_F_XS_YS#1(plus, fibs_2(z0, z1, z2), z3, z4) -> c11(COND_ZIPWITH_L_F_XS_YS(const1, z3)) [1] 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) [0] zipwith_l_f_xs_ys#1(plus, fibs_2(zipwith_l, plus, tail_l), z3, z4) -> cond_zipwith_l_f_xs_ys(ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))), z3) [0] zipwith_l_f_xs_ys#1(plus, fibs_2(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(const1, z3) [0] zipwith_l_f_xs_ys#1(plus, zipwith_l_f_xs_ys(plus, fibs, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z2), z3) [0] zipwith_l_f_xs_ys#1(plus, zipwith_l_f_xs_ys(plus, fibs_2(z05, z15, z25), z2), z3, z4) -> cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z05, z15, z25, bot[7]), z2), z3) [0] zipwith_l_f_xs_ys#1(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z06, z16, z26), z2), z3, z4) -> cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z06, z16, z26, bot[7]), z2), z3) [0] zipwith_l_f_xs_ys#1(plus, zipwith_l_f_xs_ys(z0, z1, z2), z3, z4) -> cond_zipwith_l_f_xs_ys(const1, z3) [0] cond_zipwith_l_f_xs_ys(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs, z4)) -> cond_zipwith_l_f_xs_ys_1(cond_zipwith_l_f_xs_ys(ConsL(0, fibs_2(zipwith_l, plus, tail_l)), z4), z0, z1) [0] cond_zipwith_l_f_xs_ys(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, fibs_2(z07, z17, z27), z4)) -> cond_zipwith_l_f_xs_ys_1(cond_zipwith_l_f_xs_ys(fibs_2#1(z07, z17, z27, bot[7]), z4), z0, z1) [0] cond_zipwith_l_f_xs_ys(ConsL(z0, z1), zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(z08, z18, z28), z4)) -> cond_zipwith_l_f_xs_ys_1(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z08, z18, z28, bot[7]), z4), z0, z1) [0] cond_zipwith_l_f_xs_ys(ConsL(z0, z1), zipwith_l_f_xs_ys(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(const1, z0, z1) [0] cond_zipwith_l_f_xs_ys(ConsL(z0, z1), 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))), z0, z1) [0] cond_zipwith_l_f_xs_ys(ConsL(z0, z1), fibs_2(z2, z3, z4)) -> cond_zipwith_l_f_xs_ys_1(const1, z0, z1) [0] cond_zipwith_l_f_xs_ys_1(ConsL(z0, z1), z2, z3) -> ConsL(plus#2(z2, z0), zipwith_l#3(z3, z1)) [0] fibs_2#1(zipwith_l, plus, tail_l, z0) -> ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))) [0] zipwith_l#3(z0, z1) -> zipwith_l_f_xs_ys(plus, z0, z1) [0] plus#2(0, z0) -> z0 [0] plus#2(S(z0), z1) -> S(plus#2(z0, z1)) [0] zipwith_l_f_xs_ys#1(v0, v1, v2, v3) -> const1 [0] cond_zipwith_l_f_xs_ys(v0, v1) -> const1 [0] cond_zipwith_l_f_xs_ys_1(v0, v1, v2) -> const1 [0] fibs_2#1(v0, v1, v2, v3) -> const1 [0] zipwith_l#3(v0, v1) -> fibs [0] plus#2(v0, v1) -> 0 [0] The TRS has the following type information: COND_TAKE_L_N_XS :: ConsL:const1 -> S:0 -> c3:c2 ConsL :: S:0 -> zipwith_l_f_xs_ys:fibs:fibs_2 -> ConsL:const1 zipwith_l_f_xs_ys :: plus -> zipwith_l_f_xs_ys:fibs:fibs_2 -> zipwith_l_f_xs_ys:fibs:fibs_2 -> zipwith_l_f_xs_ys:fibs:fibs_2 S :: S:0 -> S:0 c3 :: c3:c2 -> c10:c12:c11 -> c3:c2 zipwith_l_f_xs_ys#1 :: plus -> zipwith_l_f_xs_ys:fibs:fibs_2 -> zipwith_l_f_xs_ys:fibs:fibs_2 -> bot[0]:bot[6]:bot[7] -> ConsL:const1 bot[0] :: bot[0]:bot[6]:bot[7] ZIPWITH_L_F_XS_YS#1 :: plus -> zipwith_l_f_xs_ys:fibs:fibs_2 -> zipwith_l_f_xs_ys:fibs:fibs_2 -> bot[0]:bot[6]:bot[7] -> c10:c12:c11 PLUS#2 :: S:0 -> S:0 -> c5 c5 :: c5 -> c5 COND_ZIPWITH_L_F_XS_YS_1 :: ConsL:const1 -> S:0 -> zipwith_l_f_xs_ys:fibs:fibs_2 -> c6 c6 :: c5 -> c6 COND_ZIPWITH_L_F_XS_YS :: ConsL:const1 -> zipwith_l_f_xs_ys:fibs:fibs_2 -> c8:c9 c8 :: c6 -> c10:c12:c11 -> c8:c9 bot[6] :: bot[0]:bot[6]:bot[7] plus :: plus fibs :: zipwith_l_f_xs_ys:fibs:fibs_2 c10 :: c8:c9 -> c10:c12:c11 0 :: S:0 fibs_2 :: zipwith_l -> plus -> tail_l -> zipwith_l_f_xs_ys:fibs:fibs_2 zipwith_l :: zipwith_l tail_l :: tail_l c12 :: c8:c9 -> c10:c12:c11 -> c10:c12:c11 bot[7] :: bot[0]:bot[6]:bot[7] c2 :: c3:c2 -> c3:c2 fibs_2#1 :: zipwith_l -> plus -> tail_l -> bot[0]:bot[6]:bot[7] -> ConsL:const1 c9 :: c6 -> c8:c9 c11 :: c8:c9 -> c10:c12:c11 cond_zipwith_l_f_xs_ys :: ConsL:const1 -> zipwith_l_f_xs_ys:fibs:fibs_2 -> ConsL:const1 cond_zipwith_l_f_xs_ys_1 :: ConsL:const1 -> S:0 -> zipwith_l_f_xs_ys:fibs:fibs_2 -> ConsL:const1 plus#2 :: S:0 -> S:0 -> S:0 zipwith_l#3 :: zipwith_l_f_xs_ys:fibs:fibs_2 -> zipwith_l_f_xs_ys:fibs:fibs_2 -> zipwith_l_f_xs_ys:fibs:fibs_2 const1 :: ConsL:const1 const :: c3:c2 const2 :: c10:c12:c11 const3 :: c5 const4 :: c6 const5 :: c8:c9 Rewrite Strategy: INNERMOST ---------------------------------------- (35) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID)) Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction. The constant constructors are abstracted as follows: bot[0] => 0 bot[6] => 1 plus => 0 fibs => 0 0 => 0 zipwith_l => 0 tail_l => 0 bot[7] => 2 const1 => 0 const => 0 const2 => 0 const3 => 0 const4 => 0 const5 => 0 ---------------------------------------- (36) Obligation: Complexity RNTS consisting of the following rules: COND_TAKE_L_N_XS(z, z') -{ 1 }-> 1 + COND_TAKE_L_N_XS(0, z4) :|: z' = 1 + z4, z1 >= 0, z = 1 + z0 + (1 + z1 + z2 + z3), z0 >= 0, z4 >= 0, z2 >= 0, z3 >= 0 COND_TAKE_L_N_XS(z, z') -{ 1 }-> 1 + COND_TAKE_L_N_XS(1 + (1 + 0) + zipwith_l#3(0, 1 + 0 + 0 + 0), z4) :|: z' = 1 + z4, z0 >= 0, z = 1 + z0 + (1 + 0 + 0 + 0), z4 >= 0 COND_TAKE_L_N_XS(z, z') -{ 1 }-> 1 + COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0'', z1'', z2'', 2), z3), z4) + ZIPWITH_L_F_XS_YS#1(0, 1 + z0'' + z1'' + z2'', z3, 0) :|: z' = 1 + z4, z0 >= 0, z4 >= 0, z0'' >= 0, z2'' >= 0, z3 >= 0, z = 1 + z0 + (1 + 0 + (1 + z0'' + z1'' + z2'') + z3), z1'' >= 0 COND_TAKE_L_N_XS(z, z') -{ 1 }-> 1 + COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(fibs_2#1(z0', z1', z2', 2), z3), z4) + ZIPWITH_L_F_XS_YS#1(0, 1 + z0' + z1' + z2', z3, 0) :|: z' = 1 + z4, z = 1 + z0 + (1 + 0 + (1 + z0' + z1' + z2') + z3), z0' >= 0, z1' >= 0, z2' >= 0, z0 >= 0, z4 >= 0, z3 >= 0 COND_TAKE_L_N_XS(z, z') -{ 1 }-> 1 + COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(1 + 0 + (1 + 0 + 0 + 0), z3), z4) + ZIPWITH_L_F_XS_YS#1(0, 0, z3, 0) :|: z' = 1 + z4, z = 1 + z0 + (1 + 0 + 0 + z3), z0 >= 0, z4 >= 0, z3 >= 0 COND_TAKE_L_N_XS(z, z') -{ 1 }-> 1 + COND_TAKE_L_N_XS(0, z4) + ZIPWITH_L_F_XS_YS#1(z1, z2, z3, 0) :|: z' = 1 + z4, z1 >= 0, z = 1 + z0 + (1 + z1 + z2 + z3), z0 >= 0, z4 >= 0, z2 >= 0, z3 >= 0 COND_ZIPWITH_L_F_XS_YS(z, z') -{ 1 }-> 1 + COND_ZIPWITH_L_F_XS_YS_1(0, z0, z1) :|: z' = 1 + z2 + z3 + z4, z1 >= 0, z0 >= 0, z4 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0 COND_ZIPWITH_L_F_XS_YS(z, z') -{ 1 }-> 1 + COND_ZIPWITH_L_F_XS_YS_1(1 + (1 + 0) + zipwith_l#3(0, 1 + 0 + 0 + 0), z0, z1) :|: z1 >= 0, z' = 1 + 0 + 0 + 0, z0 >= 0, z = 1 + z0 + z1 COND_ZIPWITH_L_F_XS_YS(z, z') -{ 1 }-> 1 + COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z02, z12, z22, 2), z4), z0, z1) + ZIPWITH_L_F_XS_YS#1(0, 1 + z02 + z12 + z22, z4, 1) :|: z1 >= 0, z02 >= 0, z0 >= 0, z12 >= 0, z' = 1 + 0 + (1 + z02 + z12 + z22) + z4, z4 >= 0, z22 >= 0, z = 1 + z0 + z1 COND_ZIPWITH_L_F_XS_YS(z, z') -{ 1 }-> 1 + COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(fibs_2#1(z01, z11, z21, 2), z4), z0, z1) + ZIPWITH_L_F_XS_YS#1(0, 1 + z01 + z11 + z21, z4, 1) :|: z21 >= 0, z' = 1 + 0 + (1 + z01 + z11 + z21) + z4, z1 >= 0, z11 >= 0, z01 >= 0, z0 >= 0, z4 >= 0, z = 1 + z0 + z1 COND_ZIPWITH_L_F_XS_YS(z, z') -{ 1 }-> 1 + COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(1 + 0 + (1 + 0 + 0 + 0), z4), z0, z1) + ZIPWITH_L_F_XS_YS#1(0, 0, z4, 1) :|: z1 >= 0, z0 >= 0, z4 >= 0, z = 1 + z0 + z1, z' = 1 + 0 + 0 + z4 COND_ZIPWITH_L_F_XS_YS(z, z') -{ 1 }-> 1 + COND_ZIPWITH_L_F_XS_YS_1(0, z0, z1) + ZIPWITH_L_F_XS_YS#1(z2, z3, z4, 1) :|: z' = 1 + z2 + z3 + z4, z1 >= 0, z0 >= 0, z4 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0 COND_ZIPWITH_L_F_XS_YS_1(z, z', z'') -{ 1 }-> 1 + PLUS#2(z2, z0) :|: z1 >= 0, z' = z2, z0 >= 0, z'' = z3, z = 1 + z0 + z1, z2 >= 0, z3 >= 0 PLUS#2(z, z') -{ 1 }-> 1 + PLUS#2(z0, z1) :|: z1 >= 0, z = 1 + z0, z' = z1, z0 >= 0 ZIPWITH_L_F_XS_YS#1(z, z', z'', z5) -{ 1 }-> 1 + COND_ZIPWITH_L_F_XS_YS(0, z3) :|: z1 >= 0, z' = 1 + z0 + z1 + z2, z5 = z4, z0 >= 0, z'' = z3, z4 >= 0, z = 0, z2 >= 0, z3 >= 0 ZIPWITH_L_F_XS_YS#1(z, z', z'', z5) -{ 1 }-> 1 + COND_ZIPWITH_L_F_XS_YS(1 + 0 + (1 + 0 + 0 + 0), z0) :|: z1 >= 0, z'' = z0, z0 >= 0, z = 0, z' = 0, z5 = z1 ZIPWITH_L_F_XS_YS#1(z, z', z'', z5) -{ 1 }-> 1 + COND_ZIPWITH_L_F_XS_YS(1 + (1 + 0) + zipwith_l#3(0, 1 + 0 + 0 + 0), z3) :|: z' = 1 + 0 + 0 + 0, z5 = z4, z'' = z3, z4 >= 0, z = 0, z3 >= 0 ZIPWITH_L_F_XS_YS#1(z, z', z'', z5) -{ 1 }-> 1 + COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z04, z14, z24, 2), z2), z3) + ZIPWITH_L_F_XS_YS#1(0, 1 + z04 + z14 + z24, z2, 2) :|: z04 >= 0, z' = 1 + 0 + (1 + z04 + z14 + z24) + z2, z5 = z4, z'' = z3, z4 >= 0, z24 >= 0, z = 0, z14 >= 0, z2 >= 0, z3 >= 0 ZIPWITH_L_F_XS_YS#1(z, z', z'', z5) -{ 1 }-> 1 + COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(fibs_2#1(z03, z13, z23, 2), z2), z3) + ZIPWITH_L_F_XS_YS#1(0, 1 + z03 + z13 + z23, z2, 2) :|: z5 = z4, z23 >= 0, z' = 1 + 0 + (1 + z03 + z13 + z23) + z2, z'' = z3, z4 >= 0, z03 >= 0, z = 0, z13 >= 0, z2 >= 0, z3 >= 0 ZIPWITH_L_F_XS_YS#1(z, z', z'', z5) -{ 1 }-> 1 + COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(1 + 0 + (1 + 0 + 0 + 0), z2), z3) + ZIPWITH_L_F_XS_YS#1(0, 0, z2, 2) :|: z5 = z4, z'' = z3, z4 >= 0, z' = 1 + 0 + 0 + z2, z = 0, z2 >= 0, z3 >= 0 ZIPWITH_L_F_XS_YS#1(z, z', z'', z5) -{ 1 }-> 1 + COND_ZIPWITH_L_F_XS_YS(0, z3) + ZIPWITH_L_F_XS_YS#1(z0, z1, z2, 2) :|: z1 >= 0, z' = 1 + z0 + z1 + z2, z5 = z4, z0 >= 0, z'' = z3, z4 >= 0, z = 0, z2 >= 0, z3 >= 0 cond_zipwith_l_f_xs_ys(z, z') -{ 0 }-> cond_zipwith_l_f_xs_ys_1(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z08, z18, z28, 2), z4), z0, z1) :|: z08 >= 0, z18 >= 0, z1 >= 0, z28 >= 0, z' = 1 + 0 + (1 + z08 + z18 + z28) + z4, z0 >= 0, z4 >= 0, z = 1 + z0 + z1 cond_zipwith_l_f_xs_ys(z, z') -{ 0 }-> cond_zipwith_l_f_xs_ys_1(cond_zipwith_l_f_xs_ys(fibs_2#1(z07, z17, z27, 2), z4), z0, z1) :|: z1 >= 0, z07 >= 0, z17 >= 0, z27 >= 0, z0 >= 0, z' = 1 + 0 + (1 + z07 + z17 + z27) + z4, z4 >= 0, z = 1 + z0 + z1 cond_zipwith_l_f_xs_ys(z, z') -{ 0 }-> cond_zipwith_l_f_xs_ys_1(cond_zipwith_l_f_xs_ys(1 + 0 + (1 + 0 + 0 + 0), z4), z0, z1) :|: z1 >= 0, z0 >= 0, z4 >= 0, z = 1 + z0 + z1, z' = 1 + 0 + 0 + z4 cond_zipwith_l_f_xs_ys(z, z') -{ 0 }-> cond_zipwith_l_f_xs_ys_1(0, z0, z1) :|: z' = 1 + z2 + z3 + z4, z1 >= 0, z0 >= 0, z4 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0 cond_zipwith_l_f_xs_ys(z, z') -{ 0 }-> cond_zipwith_l_f_xs_ys_1(1 + (1 + 0) + zipwith_l#3(0, 1 + 0 + 0 + 0), z0, z1) :|: z1 >= 0, z' = 1 + 0 + 0 + 0, z0 >= 0, z = 1 + z0 + z1 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'') -{ 0 }-> 1 + plus#2(z2, z0) + zipwith_l#3(z3, z1) :|: z1 >= 0, z' = z2, z0 >= 0, z'' = z3, z = 1 + z0 + z1, z2 >= 0, z3 >= 0 fibs_2#1(z, z', z'', z5) -{ 0 }-> 0 :|: z5 = v3, v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0, v3 >= 0 fibs_2#1(z, z', z'', z5) -{ 0 }-> 1 + (1 + 0) + zipwith_l#3(0, 1 + 0 + 0 + 0) :|: z'' = 0, z0 >= 0, z = 0, z5 = z0, z' = 0 plus#2(z, z') -{ 0 }-> z0 :|: z0 >= 0, z = 0, z' = z0 plus#2(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 plus#2(z, z') -{ 0 }-> 1 + plus#2(z0, z1) :|: z1 >= 0, z = 1 + z0, z' = z1, z0 >= 0 zipwith_l#3(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 zipwith_l#3(z, z') -{ 0 }-> 1 + 0 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 zipwith_l_f_xs_ys#1(z, z', z'', z5) -{ 0 }-> cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z06, z16, z26, 2), z2), z3) :|: z5 = z4, z26 >= 0, z06 >= 0, z16 >= 0, z'' = z3, z4 >= 0, z = 0, z2 >= 0, z3 >= 0, z' = 1 + 0 + (1 + z06 + z16 + z26) + z2 zipwith_l_f_xs_ys#1(z, z', z'', z5) -{ 0 }-> cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(fibs_2#1(z05, z15, z25, 2), z2), z3) :|: z25 >= 0, z' = 1 + 0 + (1 + z05 + z15 + z25) + z2, z15 >= 0, z5 = z4, z'' = z3, z4 >= 0, z05 >= 0, z = 0, z2 >= 0, z3 >= 0 zipwith_l_f_xs_ys#1(z, z', z'', z5) -{ 0 }-> cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(1 + 0 + (1 + 0 + 0 + 0), z2), z3) :|: z5 = z4, z'' = z3, z4 >= 0, z' = 1 + 0 + 0 + z2, z = 0, z2 >= 0, z3 >= 0 zipwith_l_f_xs_ys#1(z, z', z'', z5) -{ 0 }-> cond_zipwith_l_f_xs_ys(0, z3) :|: z1 >= 0, z' = 1 + z0 + z1 + z2, z5 = z4, z0 >= 0, z'' = z3, z4 >= 0, z = 0, z2 >= 0, z3 >= 0 zipwith_l_f_xs_ys#1(z, z', z'', z5) -{ 0 }-> cond_zipwith_l_f_xs_ys(1 + 0 + (1 + 0 + 0 + 0), z0) :|: z1 >= 0, z'' = z0, z0 >= 0, z = 0, z' = 0, z5 = z1 zipwith_l_f_xs_ys#1(z, z', z'', z5) -{ 0 }-> cond_zipwith_l_f_xs_ys(1 + (1 + 0) + zipwith_l#3(0, 1 + 0 + 0 + 0), z3) :|: z' = 1 + 0 + 0 + 0, z5 = z4, z'' = z3, z4 >= 0, z = 0, z3 >= 0 zipwith_l_f_xs_ys#1(z, z', z'', z5) -{ 0 }-> 0 :|: z5 = v3, v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0, v3 >= 0 ---------------------------------------- (37) InliningProof (UPPER BOUND(ID)) Inlined the following terminating rules on right-hand sides where appropriate: zipwith_l#3(z, z') -{ 0 }-> 1 + 0 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 zipwith_l#3(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 fibs_2#1(z, z', z'', z5) -{ 0 }-> 1 + (1 + 0) + zipwith_l#3(0, 1 + 0 + 0 + 0) :|: z'' = 0, z0 >= 0, z = 0, z5 = z0, z' = 0 fibs_2#1(z, z', z'', z5) -{ 0 }-> 0 :|: z5 = v3, v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0, v3 >= 0 ---------------------------------------- (38) Obligation: Complexity RNTS consisting of the following rules: COND_TAKE_L_N_XS(z, z') -{ 1 }-> 1 + COND_TAKE_L_N_XS(0, z4) :|: z' = 1 + z4, z1 >= 0, z = 1 + z0 + (1 + z1 + z2 + z3), z0 >= 0, z4 >= 0, z2 >= 0, z3 >= 0 COND_TAKE_L_N_XS(z, z') -{ 1 }-> 1 + COND_TAKE_L_N_XS(1 + (1 + 0) + 0, z4) :|: z' = 1 + z4, z0 >= 0, z = 1 + z0 + (1 + 0 + 0 + 0), z4 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 1 + 0 + 0 + 0 = v1 COND_TAKE_L_N_XS(z, z') -{ 1 }-> 1 + COND_TAKE_L_N_XS(1 + (1 + 0) + (1 + 0 + z0' + z1), z4) :|: z' = 1 + z4, z0 >= 0, z = 1 + z0 + (1 + 0 + 0 + 0), z4 >= 0, 0 = z0', z1 >= 0, 1 + 0 + 0 + 0 = z1, z0' >= 0 COND_TAKE_L_N_XS(z, z') -{ 1 }-> 1 + COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0'', z1'', z2'', 2), z3), z4) + ZIPWITH_L_F_XS_YS#1(0, 1 + z0'' + z1'' + z2'', z3, 0) :|: z' = 1 + z4, z0 >= 0, z4 >= 0, z0'' >= 0, z2'' >= 0, z3 >= 0, z = 1 + z0 + (1 + 0 + (1 + z0'' + z1'' + z2'') + z3), z1'' >= 0 COND_TAKE_L_N_XS(z, z') -{ 1 }-> 1 + COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(0, z3), z4) + ZIPWITH_L_F_XS_YS#1(0, 1 + z0' + z1' + z2', z3, 0) :|: z' = 1 + z4, z = 1 + z0 + (1 + 0 + (1 + z0' + z1' + z2') + z3), z0' >= 0, z1' >= 0, z2' >= 0, z0 >= 0, z4 >= 0, z3 >= 0, 2 = v3, v0 >= 0, z2' = v2, v1 >= 0, z0' = v0, z1' = v1, v2 >= 0, v3 >= 0 COND_TAKE_L_N_XS(z, z') -{ 1 }-> 1 + COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(1 + 0 + (1 + 0 + 0 + 0), z3), z4) + ZIPWITH_L_F_XS_YS#1(0, 0, z3, 0) :|: z' = 1 + z4, z = 1 + z0 + (1 + 0 + 0 + z3), z0 >= 0, z4 >= 0, z3 >= 0 COND_TAKE_L_N_XS(z, z') -{ 1 }-> 1 + COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(1 + (1 + 0) + zipwith_l#3(0, 1 + 0 + 0 + 0), z3), z4) + ZIPWITH_L_F_XS_YS#1(0, 1 + z0' + z1' + z2', z3, 0) :|: z' = 1 + z4, z = 1 + z0 + (1 + 0 + (1 + z0' + z1' + z2') + z3), z0' >= 0, z1' >= 0, z2' >= 0, z0 >= 0, z4 >= 0, z3 >= 0, z2' = 0, z0'' >= 0, z0' = 0, 2 = z0'', z1' = 0 COND_TAKE_L_N_XS(z, z') -{ 1 }-> 1 + COND_TAKE_L_N_XS(0, z4) + ZIPWITH_L_F_XS_YS#1(z1, z2, z3, 0) :|: z' = 1 + z4, z1 >= 0, z = 1 + z0 + (1 + z1 + z2 + z3), z0 >= 0, z4 >= 0, z2 >= 0, z3 >= 0 COND_ZIPWITH_L_F_XS_YS(z, z') -{ 1 }-> 1 + COND_ZIPWITH_L_F_XS_YS_1(0, z0, z1) :|: z' = 1 + z2 + z3 + z4, z1 >= 0, z0 >= 0, z4 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0 COND_ZIPWITH_L_F_XS_YS(z, z') -{ 1 }-> 1 + COND_ZIPWITH_L_F_XS_YS_1(1 + (1 + 0) + 0, z0, z1) :|: z1 >= 0, z' = 1 + 0 + 0 + 0, z0 >= 0, z = 1 + z0 + z1, v0 >= 0, v1 >= 0, 0 = v0, 1 + 0 + 0 + 0 = v1 COND_ZIPWITH_L_F_XS_YS(z, z') -{ 1 }-> 1 + COND_ZIPWITH_L_F_XS_YS_1(1 + (1 + 0) + (1 + 0 + z0' + z1'), z0, z1) :|: z1 >= 0, z' = 1 + 0 + 0 + 0, z0 >= 0, z = 1 + z0 + z1, 0 = z0', z1' >= 0, 1 + 0 + 0 + 0 = z1', z0' >= 0 COND_ZIPWITH_L_F_XS_YS(z, z') -{ 1 }-> 1 + COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z02, z12, z22, 2), z4), z0, z1) + ZIPWITH_L_F_XS_YS#1(0, 1 + z02 + z12 + z22, z4, 1) :|: z1 >= 0, z02 >= 0, z0 >= 0, z12 >= 0, z' = 1 + 0 + (1 + z02 + z12 + z22) + z4, z4 >= 0, z22 >= 0, z = 1 + z0 + z1 COND_ZIPWITH_L_F_XS_YS(z, z') -{ 1 }-> 1 + COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(0, z4), z0, z1) + ZIPWITH_L_F_XS_YS#1(0, 1 + z01 + z11 + z21, z4, 1) :|: z21 >= 0, z' = 1 + 0 + (1 + z01 + z11 + z21) + z4, z1 >= 0, z11 >= 0, z01 >= 0, z0 >= 0, z4 >= 0, z = 1 + z0 + z1, 2 = v3, v0 >= 0, z21 = v2, v1 >= 0, z01 = v0, z11 = v1, v2 >= 0, v3 >= 0 COND_ZIPWITH_L_F_XS_YS(z, z') -{ 1 }-> 1 + COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(1 + 0 + (1 + 0 + 0 + 0), z4), z0, z1) + ZIPWITH_L_F_XS_YS#1(0, 0, z4, 1) :|: z1 >= 0, z0 >= 0, z4 >= 0, z = 1 + z0 + z1, z' = 1 + 0 + 0 + z4 COND_ZIPWITH_L_F_XS_YS(z, z') -{ 1 }-> 1 + COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(1 + (1 + 0) + zipwith_l#3(0, 1 + 0 + 0 + 0), z4), z0, z1) + ZIPWITH_L_F_XS_YS#1(0, 1 + z01 + z11 + z21, z4, 1) :|: z21 >= 0, z' = 1 + 0 + (1 + z01 + z11 + z21) + z4, z1 >= 0, z11 >= 0, z01 >= 0, z0 >= 0, z4 >= 0, z = 1 + z0 + z1, z21 = 0, z0' >= 0, z01 = 0, 2 = z0', z11 = 0 COND_ZIPWITH_L_F_XS_YS(z, z') -{ 1 }-> 1 + COND_ZIPWITH_L_F_XS_YS_1(0, z0, z1) + ZIPWITH_L_F_XS_YS#1(z2, z3, z4, 1) :|: z' = 1 + z2 + z3 + z4, z1 >= 0, z0 >= 0, z4 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0 COND_ZIPWITH_L_F_XS_YS_1(z, z', z'') -{ 1 }-> 1 + PLUS#2(z2, z0) :|: z1 >= 0, z' = z2, z0 >= 0, z'' = z3, z = 1 + z0 + z1, z2 >= 0, z3 >= 0 PLUS#2(z, z') -{ 1 }-> 1 + PLUS#2(z0, z1) :|: z1 >= 0, z = 1 + z0, z' = z1, z0 >= 0 ZIPWITH_L_F_XS_YS#1(z, z', z'', z5) -{ 1 }-> 1 + COND_ZIPWITH_L_F_XS_YS(0, z3) :|: z1 >= 0, z' = 1 + z0 + z1 + z2, z5 = z4, z0 >= 0, z'' = z3, z4 >= 0, z = 0, z2 >= 0, z3 >= 0 ZIPWITH_L_F_XS_YS#1(z, z', z'', z5) -{ 1 }-> 1 + COND_ZIPWITH_L_F_XS_YS(1 + 0 + (1 + 0 + 0 + 0), z0) :|: z1 >= 0, z'' = z0, z0 >= 0, z = 0, z' = 0, z5 = z1 ZIPWITH_L_F_XS_YS#1(z, z', z'', z5) -{ 1 }-> 1 + COND_ZIPWITH_L_F_XS_YS(1 + (1 + 0) + 0, z3) :|: z' = 1 + 0 + 0 + 0, z5 = z4, z'' = z3, z4 >= 0, z = 0, z3 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 1 + 0 + 0 + 0 = v1 ZIPWITH_L_F_XS_YS#1(z, z', z'', z5) -{ 1 }-> 1 + COND_ZIPWITH_L_F_XS_YS(1 + (1 + 0) + (1 + 0 + z0 + z1), z3) :|: z' = 1 + 0 + 0 + 0, z5 = z4, z'' = z3, z4 >= 0, z = 0, z3 >= 0, 0 = z0, z1 >= 0, 1 + 0 + 0 + 0 = z1, z0 >= 0 ZIPWITH_L_F_XS_YS#1(z, z', z'', z5) -{ 1 }-> 1 + COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z04, z14, z24, 2), z2), z3) + ZIPWITH_L_F_XS_YS#1(0, 1 + z04 + z14 + z24, z2, 2) :|: z04 >= 0, z' = 1 + 0 + (1 + z04 + z14 + z24) + z2, z5 = z4, z'' = z3, z4 >= 0, z24 >= 0, z = 0, z14 >= 0, z2 >= 0, z3 >= 0 ZIPWITH_L_F_XS_YS#1(z, z', z'', z5) -{ 1 }-> 1 + COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(0, z2), z3) + ZIPWITH_L_F_XS_YS#1(0, 1 + z03 + z13 + z23, z2, 2) :|: z5 = z4, z23 >= 0, z' = 1 + 0 + (1 + z03 + z13 + z23) + z2, z'' = z3, z4 >= 0, z03 >= 0, z = 0, z13 >= 0, z2 >= 0, z3 >= 0, 2 = v3, v0 >= 0, z23 = v2, v1 >= 0, z03 = v0, z13 = v1, v2 >= 0, v3 >= 0 ZIPWITH_L_F_XS_YS#1(z, z', z'', z5) -{ 1 }-> 1 + COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(1 + 0 + (1 + 0 + 0 + 0), z2), z3) + ZIPWITH_L_F_XS_YS#1(0, 0, z2, 2) :|: z5 = z4, z'' = z3, z4 >= 0, z' = 1 + 0 + 0 + z2, z = 0, z2 >= 0, z3 >= 0 ZIPWITH_L_F_XS_YS#1(z, z', z'', z5) -{ 1 }-> 1 + COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(1 + (1 + 0) + zipwith_l#3(0, 1 + 0 + 0 + 0), z2), z3) + ZIPWITH_L_F_XS_YS#1(0, 1 + z03 + z13 + z23, z2, 2) :|: z5 = z4, z23 >= 0, z' = 1 + 0 + (1 + z03 + z13 + z23) + z2, z'' = z3, z4 >= 0, z03 >= 0, z = 0, z13 >= 0, z2 >= 0, z3 >= 0, z23 = 0, z0 >= 0, z03 = 0, 2 = z0, z13 = 0 ZIPWITH_L_F_XS_YS#1(z, z', z'', z5) -{ 1 }-> 1 + COND_ZIPWITH_L_F_XS_YS(0, z3) + ZIPWITH_L_F_XS_YS#1(z0, z1, z2, 2) :|: z1 >= 0, z' = 1 + z0 + z1 + z2, z5 = z4, z0 >= 0, z'' = z3, z4 >= 0, z = 0, z2 >= 0, z3 >= 0 cond_zipwith_l_f_xs_ys(z, z') -{ 0 }-> cond_zipwith_l_f_xs_ys_1(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z08, z18, z28, 2), z4), z0, z1) :|: z08 >= 0, z18 >= 0, z1 >= 0, z28 >= 0, z' = 1 + 0 + (1 + z08 + z18 + z28) + z4, z0 >= 0, z4 >= 0, z = 1 + z0 + z1 cond_zipwith_l_f_xs_ys(z, z') -{ 0 }-> cond_zipwith_l_f_xs_ys_1(cond_zipwith_l_f_xs_ys(0, z4), z0, z1) :|: z1 >= 0, z07 >= 0, z17 >= 0, z27 >= 0, z0 >= 0, z' = 1 + 0 + (1 + z07 + z17 + z27) + z4, z4 >= 0, z = 1 + z0 + z1, 2 = v3, v0 >= 0, z27 = v2, v1 >= 0, z07 = v0, z17 = v1, v2 >= 0, v3 >= 0 cond_zipwith_l_f_xs_ys(z, z') -{ 0 }-> cond_zipwith_l_f_xs_ys_1(cond_zipwith_l_f_xs_ys(1 + 0 + (1 + 0 + 0 + 0), z4), z0, z1) :|: z1 >= 0, z0 >= 0, z4 >= 0, z = 1 + z0 + z1, z' = 1 + 0 + 0 + z4 cond_zipwith_l_f_xs_ys(z, z') -{ 0 }-> cond_zipwith_l_f_xs_ys_1(cond_zipwith_l_f_xs_ys(1 + (1 + 0) + zipwith_l#3(0, 1 + 0 + 0 + 0), z4), z0, z1) :|: z1 >= 0, z07 >= 0, z17 >= 0, z27 >= 0, z0 >= 0, z' = 1 + 0 + (1 + z07 + z17 + z27) + z4, z4 >= 0, z = 1 + z0 + z1, z27 = 0, z0' >= 0, z07 = 0, 2 = z0', z17 = 0 cond_zipwith_l_f_xs_ys(z, z') -{ 0 }-> cond_zipwith_l_f_xs_ys_1(0, z0, z1) :|: z' = 1 + z2 + z3 + z4, z1 >= 0, z0 >= 0, z4 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0 cond_zipwith_l_f_xs_ys(z, z') -{ 0 }-> cond_zipwith_l_f_xs_ys_1(1 + (1 + 0) + 0, z0, z1) :|: z1 >= 0, z' = 1 + 0 + 0 + 0, z0 >= 0, z = 1 + z0 + z1, v0 >= 0, v1 >= 0, 0 = v0, 1 + 0 + 0 + 0 = v1 cond_zipwith_l_f_xs_ys(z, z') -{ 0 }-> cond_zipwith_l_f_xs_ys_1(1 + (1 + 0) + (1 + 0 + z0' + z1'), z0, z1) :|: z1 >= 0, z' = 1 + 0 + 0 + 0, z0 >= 0, z = 1 + z0 + z1, 0 = z0', z1' >= 0, 1 + 0 + 0 + 0 = z1', z0' >= 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'') -{ 0 }-> 1 + plus#2(z2, z0) + 0 :|: z1 >= 0, z' = z2, z0 >= 0, z'' = z3, z = 1 + z0 + z1, z2 >= 0, z3 >= 0, v0 >= 0, v1 >= 0, z3 = v0, z1 = v1 cond_zipwith_l_f_xs_ys_1(z, z', z'') -{ 0 }-> 1 + plus#2(z2, z0) + (1 + 0 + z0' + z1') :|: z1 >= 0, z' = z2, z0 >= 0, z'' = z3, z = 1 + z0 + z1, z2 >= 0, z3 >= 0, z3 = z0', z1' >= 0, z1 = z1', z0' >= 0 fibs_2#1(z, z', z'', z5) -{ 0 }-> 0 :|: z5 = v3, v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0, v3 >= 0 fibs_2#1(z, z', z'', z5) -{ 0 }-> 1 + (1 + 0) + 0 :|: z'' = 0, z0 >= 0, z = 0, z5 = z0, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 1 + 0 + 0 + 0 = v1 fibs_2#1(z, z', z'', z5) -{ 0 }-> 1 + (1 + 0) + (1 + 0 + z0' + z1) :|: z'' = 0, z0 >= 0, z = 0, z5 = z0, z' = 0, 0 = z0', z1 >= 0, 1 + 0 + 0 + 0 = z1, z0' >= 0 plus#2(z, z') -{ 0 }-> z0 :|: z0 >= 0, z = 0, z' = z0 plus#2(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 plus#2(z, z') -{ 0 }-> 1 + plus#2(z0, z1) :|: z1 >= 0, z = 1 + z0, z' = z1, z0 >= 0 zipwith_l#3(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 zipwith_l#3(z, z') -{ 0 }-> 1 + 0 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 zipwith_l_f_xs_ys#1(z, z', z'', z5) -{ 0 }-> cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z06, z16, z26, 2), z2), z3) :|: z5 = z4, z26 >= 0, z06 >= 0, z16 >= 0, z'' = z3, z4 >= 0, z = 0, z2 >= 0, z3 >= 0, z' = 1 + 0 + (1 + z06 + z16 + z26) + z2 zipwith_l_f_xs_ys#1(z, z', z'', z5) -{ 0 }-> cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(0, z2), z3) :|: z25 >= 0, z' = 1 + 0 + (1 + z05 + z15 + z25) + z2, z15 >= 0, z5 = z4, z'' = z3, z4 >= 0, z05 >= 0, z = 0, z2 >= 0, z3 >= 0, 2 = v3, v0 >= 0, z25 = v2, v1 >= 0, z05 = v0, z15 = v1, v2 >= 0, v3 >= 0 zipwith_l_f_xs_ys#1(z, z', z'', z5) -{ 0 }-> cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(1 + 0 + (1 + 0 + 0 + 0), z2), z3) :|: z5 = z4, z'' = z3, z4 >= 0, z' = 1 + 0 + 0 + z2, z = 0, z2 >= 0, z3 >= 0 zipwith_l_f_xs_ys#1(z, z', z'', z5) -{ 0 }-> cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(1 + (1 + 0) + zipwith_l#3(0, 1 + 0 + 0 + 0), z2), z3) :|: z25 >= 0, z' = 1 + 0 + (1 + z05 + z15 + z25) + z2, z15 >= 0, z5 = z4, z'' = z3, z4 >= 0, z05 >= 0, z = 0, z2 >= 0, z3 >= 0, z25 = 0, z0 >= 0, z05 = 0, 2 = z0, z15 = 0 zipwith_l_f_xs_ys#1(z, z', z'', z5) -{ 0 }-> cond_zipwith_l_f_xs_ys(0, z3) :|: z1 >= 0, z' = 1 + z0 + z1 + z2, z5 = z4, z0 >= 0, z'' = z3, z4 >= 0, z = 0, z2 >= 0, z3 >= 0 zipwith_l_f_xs_ys#1(z, z', z'', z5) -{ 0 }-> cond_zipwith_l_f_xs_ys(1 + 0 + (1 + 0 + 0 + 0), z0) :|: z1 >= 0, z'' = z0, z0 >= 0, z = 0, z' = 0, z5 = z1 zipwith_l_f_xs_ys#1(z, z', z'', z5) -{ 0 }-> cond_zipwith_l_f_xs_ys(1 + (1 + 0) + 0, z3) :|: z' = 1 + 0 + 0 + 0, z5 = z4, z'' = z3, z4 >= 0, z = 0, z3 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 1 + 0 + 0 + 0 = v1 zipwith_l_f_xs_ys#1(z, z', z'', z5) -{ 0 }-> cond_zipwith_l_f_xs_ys(1 + (1 + 0) + (1 + 0 + z0 + z1), z3) :|: z' = 1 + 0 + 0 + 0, z5 = z4, z'' = z3, z4 >= 0, z = 0, z3 >= 0, 0 = z0, z1 >= 0, 1 + 0 + 0 + 0 = z1, z0 >= 0 zipwith_l_f_xs_ys#1(z, z', z'', z5) -{ 0 }-> 0 :|: z5 = v3, v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0, v3 >= 0 ---------------------------------------- (39) SimplificationProof (BOTH BOUNDS(ID, ID)) Simplified the RNTS by moving equalities from the constraints into the right-hand sides. ---------------------------------------- (40) Obligation: Complexity RNTS consisting of the following rules: COND_TAKE_L_N_XS(z, z') -{ 1 }-> 1 + COND_TAKE_L_N_XS(0, z' - 1) :|: z1 >= 0, z = 1 + z0 + (1 + z1 + z2 + z3), z0 >= 0, z' - 1 >= 0, z2 >= 0, z3 >= 0 COND_TAKE_L_N_XS(z, z') -{ 1 }-> 1 + COND_TAKE_L_N_XS(1 + (1 + 0) + 0, z' - 1) :|: z - 2 >= 0, z' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 1 + 0 + 0 + 0 = v1 COND_TAKE_L_N_XS(z, z') -{ 1 }-> 1 + COND_TAKE_L_N_XS(1 + (1 + 0) + (1 + 0 + z0' + z1), z' - 1) :|: z - 2 >= 0, z' - 1 >= 0, 0 = z0', z1 >= 0, 1 + 0 + 0 + 0 = z1, z0' >= 0 COND_TAKE_L_N_XS(z, z') -{ 1 }-> 1 + COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0'', z1'', z2'', 2), z3), z' - 1) + ZIPWITH_L_F_XS_YS#1(0, 1 + z0'' + z1'' + z2'', z3, 0) :|: z0 >= 0, z' - 1 >= 0, z0'' >= 0, z2'' >= 0, z3 >= 0, z = 1 + z0 + (1 + 0 + (1 + z0'' + z1'' + z2'') + z3), z1'' >= 0 COND_TAKE_L_N_XS(z, z') -{ 1 }-> 1 + COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(0, z3), z' - 1) + ZIPWITH_L_F_XS_YS#1(0, 1 + z0' + z1' + z2', z3, 0) :|: z = 1 + z0 + (1 + 0 + (1 + z0' + z1' + z2') + z3), z0' >= 0, z1' >= 0, z2' >= 0, z0 >= 0, z' - 1 >= 0, z3 >= 0, 2 = v3, v0 >= 0, z2' = v2, v1 >= 0, z0' = v0, z1' = v1, v2 >= 0, v3 >= 0 COND_TAKE_L_N_XS(z, z') -{ 1 }-> 1 + COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(1 + 0 + (1 + 0 + 0 + 0), z3), z' - 1) + ZIPWITH_L_F_XS_YS#1(0, 0, z3, 0) :|: z = 1 + z0 + (1 + 0 + 0 + z3), z0 >= 0, z' - 1 >= 0, z3 >= 0 COND_TAKE_L_N_XS(z, z') -{ 1 }-> 1 + COND_TAKE_L_N_XS(cond_zipwith_l_f_xs_ys(1 + (1 + 0) + zipwith_l#3(0, 1 + 0 + 0 + 0), z3), z' - 1) + ZIPWITH_L_F_XS_YS#1(0, 1 + z0' + z1' + z2', z3, 0) :|: z = 1 + z0 + (1 + 0 + (1 + z0' + z1' + z2') + z3), z0' >= 0, z1' >= 0, z2' >= 0, z0 >= 0, z' - 1 >= 0, z3 >= 0, z2' = 0, z0'' >= 0, z0' = 0, 2 = z0'', z1' = 0 COND_TAKE_L_N_XS(z, z') -{ 1 }-> 1 + COND_TAKE_L_N_XS(0, z' - 1) + ZIPWITH_L_F_XS_YS#1(z1, z2, z3, 0) :|: z1 >= 0, z = 1 + z0 + (1 + z1 + z2 + z3), z0 >= 0, z' - 1 >= 0, z2 >= 0, z3 >= 0 COND_ZIPWITH_L_F_XS_YS(z, z') -{ 1 }-> 1 + COND_ZIPWITH_L_F_XS_YS_1(0, z0, z1) :|: z' = 1 + z2 + z3 + z4, z1 >= 0, z0 >= 0, z4 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0 COND_ZIPWITH_L_F_XS_YS(z, z') -{ 1 }-> 1 + COND_ZIPWITH_L_F_XS_YS_1(1 + (1 + 0) + 0, z0, z1) :|: z1 >= 0, z' = 1 + 0 + 0 + 0, z0 >= 0, z = 1 + z0 + z1, v0 >= 0, v1 >= 0, 0 = v0, 1 + 0 + 0 + 0 = v1 COND_ZIPWITH_L_F_XS_YS(z, z') -{ 1 }-> 1 + COND_ZIPWITH_L_F_XS_YS_1(1 + (1 + 0) + (1 + 0 + z0' + z1'), z0, z1) :|: z1 >= 0, z' = 1 + 0 + 0 + 0, z0 >= 0, z = 1 + z0 + z1, 0 = z0', z1' >= 0, 1 + 0 + 0 + 0 = z1', z0' >= 0 COND_ZIPWITH_L_F_XS_YS(z, z') -{ 1 }-> 1 + COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z02, z12, z22, 2), z4), z0, z1) + ZIPWITH_L_F_XS_YS#1(0, 1 + z02 + z12 + z22, z4, 1) :|: z1 >= 0, z02 >= 0, z0 >= 0, z12 >= 0, z' = 1 + 0 + (1 + z02 + z12 + z22) + z4, z4 >= 0, z22 >= 0, z = 1 + z0 + z1 COND_ZIPWITH_L_F_XS_YS(z, z') -{ 1 }-> 1 + COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(0, z4), z0, z1) + ZIPWITH_L_F_XS_YS#1(0, 1 + z01 + z11 + z21, z4, 1) :|: z21 >= 0, z' = 1 + 0 + (1 + z01 + z11 + z21) + z4, z1 >= 0, z11 >= 0, z01 >= 0, z0 >= 0, z4 >= 0, z = 1 + z0 + z1, 2 = v3, v0 >= 0, z21 = v2, v1 >= 0, z01 = v0, z11 = v1, v2 >= 0, v3 >= 0 COND_ZIPWITH_L_F_XS_YS(z, z') -{ 1 }-> 1 + COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(1 + 0 + (1 + 0 + 0 + 0), z' - 1), z0, z1) + ZIPWITH_L_F_XS_YS#1(0, 0, z' - 1, 1) :|: z1 >= 0, z0 >= 0, z' - 1 >= 0, z = 1 + z0 + z1 COND_ZIPWITH_L_F_XS_YS(z, z') -{ 1 }-> 1 + COND_ZIPWITH_L_F_XS_YS_1(cond_zipwith_l_f_xs_ys(1 + (1 + 0) + zipwith_l#3(0, 1 + 0 + 0 + 0), z4), z0, z1) + ZIPWITH_L_F_XS_YS#1(0, 1 + z01 + z11 + z21, z4, 1) :|: z21 >= 0, z' = 1 + 0 + (1 + z01 + z11 + z21) + z4, z1 >= 0, z11 >= 0, z01 >= 0, z0 >= 0, z4 >= 0, z = 1 + z0 + z1, z21 = 0, z0' >= 0, z01 = 0, 2 = z0', z11 = 0 COND_ZIPWITH_L_F_XS_YS(z, z') -{ 1 }-> 1 + COND_ZIPWITH_L_F_XS_YS_1(0, z0, z1) + ZIPWITH_L_F_XS_YS#1(z2, z3, z4, 1) :|: z' = 1 + z2 + z3 + z4, z1 >= 0, z0 >= 0, z4 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0 COND_ZIPWITH_L_F_XS_YS_1(z, z', z'') -{ 1 }-> 1 + PLUS#2(z', z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0, z'' >= 0 PLUS#2(z, z') -{ 1 }-> 1 + PLUS#2(z - 1, z') :|: z' >= 0, z - 1 >= 0 ZIPWITH_L_F_XS_YS#1(z, z', z'', z5) -{ 1 }-> 1 + COND_ZIPWITH_L_F_XS_YS(0, z'') :|: z1 >= 0, z' = 1 + z0 + z1 + z2, z0 >= 0, z5 >= 0, z = 0, z2 >= 0, z'' >= 0 ZIPWITH_L_F_XS_YS#1(z, z', z'', z5) -{ 1 }-> 1 + COND_ZIPWITH_L_F_XS_YS(1 + 0 + (1 + 0 + 0 + 0), z'') :|: z5 >= 0, z'' >= 0, z = 0, z' = 0 ZIPWITH_L_F_XS_YS#1(z, z', z'', z5) -{ 1 }-> 1 + COND_ZIPWITH_L_F_XS_YS(1 + (1 + 0) + 0, z'') :|: z' = 1 + 0 + 0 + 0, z5 >= 0, z = 0, z'' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 1 + 0 + 0 + 0 = v1 ZIPWITH_L_F_XS_YS#1(z, z', z'', z5) -{ 1 }-> 1 + COND_ZIPWITH_L_F_XS_YS(1 + (1 + 0) + (1 + 0 + z0 + z1), z'') :|: z' = 1 + 0 + 0 + 0, z5 >= 0, z = 0, z'' >= 0, 0 = z0, z1 >= 0, 1 + 0 + 0 + 0 = z1, z0 >= 0 ZIPWITH_L_F_XS_YS#1(z, z', z'', z5) -{ 1 }-> 1 + COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z04, z14, z24, 2), z2), z'') + ZIPWITH_L_F_XS_YS#1(0, 1 + z04 + z14 + z24, z2, 2) :|: z04 >= 0, z' = 1 + 0 + (1 + z04 + z14 + z24) + z2, z5 >= 0, z24 >= 0, z = 0, z14 >= 0, z2 >= 0, z'' >= 0 ZIPWITH_L_F_XS_YS#1(z, z', z'', z5) -{ 1 }-> 1 + COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(0, z2), z'') + ZIPWITH_L_F_XS_YS#1(0, 1 + z03 + z13 + z23, z2, 2) :|: z23 >= 0, z' = 1 + 0 + (1 + z03 + z13 + z23) + z2, z5 >= 0, z03 >= 0, z = 0, z13 >= 0, z2 >= 0, z'' >= 0, 2 = v3, v0 >= 0, z23 = v2, v1 >= 0, z03 = v0, z13 = v1, v2 >= 0, v3 >= 0 ZIPWITH_L_F_XS_YS#1(z, z', z'', z5) -{ 1 }-> 1 + COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(1 + 0 + (1 + 0 + 0 + 0), z' - 1), z'') + ZIPWITH_L_F_XS_YS#1(0, 0, z' - 1, 2) :|: z5 >= 0, z = 0, z' - 1 >= 0, z'' >= 0 ZIPWITH_L_F_XS_YS#1(z, z', z'', z5) -{ 1 }-> 1 + COND_ZIPWITH_L_F_XS_YS(cond_zipwith_l_f_xs_ys(1 + (1 + 0) + zipwith_l#3(0, 1 + 0 + 0 + 0), z2), z'') + ZIPWITH_L_F_XS_YS#1(0, 1 + z03 + z13 + z23, z2, 2) :|: z23 >= 0, z' = 1 + 0 + (1 + z03 + z13 + z23) + z2, z5 >= 0, z03 >= 0, z = 0, z13 >= 0, z2 >= 0, z'' >= 0, z23 = 0, z0 >= 0, z03 = 0, 2 = z0, z13 = 0 ZIPWITH_L_F_XS_YS#1(z, z', z'', z5) -{ 1 }-> 1 + COND_ZIPWITH_L_F_XS_YS(0, z'') + ZIPWITH_L_F_XS_YS#1(z0, z1, z2, 2) :|: z1 >= 0, z' = 1 + z0 + z1 + z2, z0 >= 0, z5 >= 0, z = 0, z2 >= 0, z'' >= 0 cond_zipwith_l_f_xs_ys(z, z') -{ 0 }-> cond_zipwith_l_f_xs_ys_1(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z08, z18, z28, 2), z4), z0, z1) :|: z08 >= 0, z18 >= 0, z1 >= 0, z28 >= 0, z' = 1 + 0 + (1 + z08 + z18 + z28) + z4, z0 >= 0, z4 >= 0, z = 1 + z0 + z1 cond_zipwith_l_f_xs_ys(z, z') -{ 0 }-> cond_zipwith_l_f_xs_ys_1(cond_zipwith_l_f_xs_ys(0, z4), z0, z1) :|: z1 >= 0, z07 >= 0, z17 >= 0, z27 >= 0, z0 >= 0, z' = 1 + 0 + (1 + z07 + z17 + z27) + z4, z4 >= 0, z = 1 + z0 + z1, 2 = v3, v0 >= 0, z27 = v2, v1 >= 0, z07 = v0, z17 = v1, v2 >= 0, v3 >= 0 cond_zipwith_l_f_xs_ys(z, z') -{ 0 }-> cond_zipwith_l_f_xs_ys_1(cond_zipwith_l_f_xs_ys(1 + 0 + (1 + 0 + 0 + 0), z' - 1), z0, z1) :|: z1 >= 0, z0 >= 0, z' - 1 >= 0, z = 1 + z0 + z1 cond_zipwith_l_f_xs_ys(z, z') -{ 0 }-> cond_zipwith_l_f_xs_ys_1(cond_zipwith_l_f_xs_ys(1 + (1 + 0) + zipwith_l#3(0, 1 + 0 + 0 + 0), z4), z0, z1) :|: z1 >= 0, z07 >= 0, z17 >= 0, z27 >= 0, z0 >= 0, z' = 1 + 0 + (1 + z07 + z17 + z27) + z4, z4 >= 0, z = 1 + z0 + z1, z27 = 0, z0' >= 0, z07 = 0, 2 = z0', z17 = 0 cond_zipwith_l_f_xs_ys(z, z') -{ 0 }-> cond_zipwith_l_f_xs_ys_1(0, z0, z1) :|: z' = 1 + z2 + z3 + z4, z1 >= 0, z0 >= 0, z4 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0 cond_zipwith_l_f_xs_ys(z, z') -{ 0 }-> cond_zipwith_l_f_xs_ys_1(1 + (1 + 0) + 0, z0, z1) :|: z1 >= 0, z' = 1 + 0 + 0 + 0, z0 >= 0, z = 1 + z0 + z1, v0 >= 0, v1 >= 0, 0 = v0, 1 + 0 + 0 + 0 = v1 cond_zipwith_l_f_xs_ys(z, z') -{ 0 }-> cond_zipwith_l_f_xs_ys_1(1 + (1 + 0) + (1 + 0 + z0' + z1'), z0, z1) :|: z1 >= 0, z' = 1 + 0 + 0 + 0, z0 >= 0, z = 1 + z0 + z1, 0 = z0', z1' >= 0, 1 + 0 + 0 + 0 = z1', z0' >= 0 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'') -{ 0 }-> 1 + plus#2(z', z0) + 0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0, z'' >= 0, v1 >= 0, z1 = v1 cond_zipwith_l_f_xs_ys_1(z, z', z'') -{ 0 }-> 1 + plus#2(z', z0) + (1 + 0 + z'' + z1') :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1, z' >= 0, z'' >= 0, z1' >= 0, z1 = z1' fibs_2#1(z, z', z'', z5) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z5 >= 0 fibs_2#1(z, z', z'', z5) -{ 0 }-> 1 + (1 + 0) + 0 :|: z'' = 0, z5 >= 0, z = 0, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 1 + 0 + 0 + 0 = v1 fibs_2#1(z, z', z'', z5) -{ 0 }-> 1 + (1 + 0) + (1 + 0 + z0' + z1) :|: z'' = 0, z5 >= 0, z = 0, z' = 0, 0 = z0', z1 >= 0, 1 + 0 + 0 + 0 = z1, z0' >= 0 plus#2(z, z') -{ 0 }-> z' :|: z' >= 0, z = 0 plus#2(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 plus#2(z, z') -{ 0 }-> 1 + plus#2(z - 1, z') :|: z' >= 0, z - 1 >= 0 zipwith_l#3(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 zipwith_l#3(z, z') -{ 0 }-> 1 + 0 + z + z' :|: z' >= 0, z >= 0 zipwith_l_f_xs_ys#1(z, z', z'', z5) -{ 0 }-> cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z06, z16, z26, 2), z2), z'') :|: z26 >= 0, z06 >= 0, z16 >= 0, z5 >= 0, z = 0, z2 >= 0, z'' >= 0, z' = 1 + 0 + (1 + z06 + z16 + z26) + z2 zipwith_l_f_xs_ys#1(z, z', z'', z5) -{ 0 }-> cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(0, z2), z'') :|: z25 >= 0, z' = 1 + 0 + (1 + z05 + z15 + z25) + z2, z15 >= 0, z5 >= 0, z05 >= 0, z = 0, z2 >= 0, z'' >= 0, 2 = v3, v0 >= 0, z25 = v2, v1 >= 0, z05 = v0, z15 = v1, v2 >= 0, v3 >= 0 zipwith_l_f_xs_ys#1(z, z', z'', z5) -{ 0 }-> cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(1 + 0 + (1 + 0 + 0 + 0), z' - 1), z'') :|: z5 >= 0, z = 0, z' - 1 >= 0, z'' >= 0 zipwith_l_f_xs_ys#1(z, z', z'', z5) -{ 0 }-> cond_zipwith_l_f_xs_ys(cond_zipwith_l_f_xs_ys(1 + (1 + 0) + zipwith_l#3(0, 1 + 0 + 0 + 0), z2), z'') :|: z25 >= 0, z' = 1 + 0 + (1 + z05 + z15 + z25) + z2, z15 >= 0, z5 >= 0, z05 >= 0, z = 0, z2 >= 0, z'' >= 0, z25 = 0, z0 >= 0, z05 = 0, 2 = z0, z15 = 0 zipwith_l_f_xs_ys#1(z, z', z'', z5) -{ 0 }-> cond_zipwith_l_f_xs_ys(0, z'') :|: z1 >= 0, z' = 1 + z0 + z1 + z2, z0 >= 0, z5 >= 0, z = 0, z2 >= 0, z'' >= 0 zipwith_l_f_xs_ys#1(z, z', z'', z5) -{ 0 }-> cond_zipwith_l_f_xs_ys(1 + 0 + (1 + 0 + 0 + 0), z'') :|: z5 >= 0, z'' >= 0, z = 0, z' = 0 zipwith_l_f_xs_ys#1(z, z', z'', z5) -{ 0 }-> cond_zipwith_l_f_xs_ys(1 + (1 + 0) + 0, z'') :|: z' = 1 + 0 + 0 + 0, z5 >= 0, z = 0, z'' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 1 + 0 + 0 + 0 = v1 zipwith_l_f_xs_ys#1(z, z', z'', z5) -{ 0 }-> cond_zipwith_l_f_xs_ys(1 + (1 + 0) + (1 + 0 + z0 + z1), z'') :|: z' = 1 + 0 + 0 + 0, z5 >= 0, z = 0, z'' >= 0, 0 = z0, z1 >= 0, 1 + 0 + 0 + 0 = z1, z0 >= 0 zipwith_l_f_xs_ys#1(z, z', z'', z5) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z5 >= 0 ---------------------------------------- (41) 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: zipwith_l_f_xs_ys#1(v0, v1, v2, v3) -> null_zipwith_l_f_xs_ys#1 [0] cond_zipwith_l_f_xs_ys(v0, v1) -> null_cond_zipwith_l_f_xs_ys [0] cond_zipwith_l_f_xs_ys_1(v0, v1, v2) -> null_cond_zipwith_l_f_xs_ys_1 [0] fibs_2#1(v0, v1, v2, v3) -> null_fibs_2#1 [0] zipwith_l#3(v0, v1) -> null_zipwith_l#3 [0] plus#2(v0, v1) -> null_plus#2 [0] COND_TAKE_L_N_XS(v0, v1) -> null_COND_TAKE_L_N_XS [0] PLUS#2(v0, v1) -> null_PLUS#2 [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] ZIPWITH_L_F_XS_YS#1(v0, v1, v2, v3) -> null_ZIPWITH_L_F_XS_YS#1 [0] And the following fresh constants: null_zipwith_l_f_xs_ys#1, null_cond_zipwith_l_f_xs_ys, null_cond_zipwith_l_f_xs_ys_1, null_fibs_2#1, null_zipwith_l#3, null_plus#2, null_COND_TAKE_L_N_XS, null_PLUS#2, null_COND_ZIPWITH_L_F_XS_YS_1, null_COND_ZIPWITH_L_F_XS_YS, null_ZIPWITH_L_F_XS_YS#1 ---------------------------------------- (42) 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: 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])) [1] PLUS#2(S(z0), z1) -> c5(PLUS#2(z0, z1)) [1] COND_ZIPWITH_L_F_XS_YS_1(ConsL(z0, z1), z2, z3) -> c6(PLUS#2(z2, z0)) [1] 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])) [1] 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)) [1] 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])) [1] 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)) [1] 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)) [1] 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)) [1] 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) [0] 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) [0] 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) [0] 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) [0] 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) [0] cond_zipwith_l_f_xs_ys_1(ConsL(z0, z1), z2, z3) -> ConsL(plus#2(z2, z0), zipwith_l#3(z3, z1)) [0] fibs_2#1(zipwith_l, plus, tail_l, z0) -> ConsL(S(0), zipwith_l#3(fibs, fibs_2(zipwith_l, plus, tail_l))) [0] zipwith_l#3(z0, z1) -> zipwith_l_f_xs_ys(plus, z0, z1) [0] plus#2(0, z0) -> z0 [0] plus#2(S(z0), z1) -> S(plus#2(z0, z1)) [0] zipwith_l_f_xs_ys#1(v0, v1, v2, v3) -> null_zipwith_l_f_xs_ys#1 [0] cond_zipwith_l_f_xs_ys(v0, v1) -> null_cond_zipwith_l_f_xs_ys [0] cond_zipwith_l_f_xs_ys_1(v0, v1, v2) -> null_cond_zipwith_l_f_xs_ys_1 [0] fibs_2#1(v0, v1, v2, v3) -> null_fibs_2#1 [0] zipwith_l#3(v0, v1) -> null_zipwith_l#3 [0] plus#2(v0, v1) -> null_plus#2 [0] COND_TAKE_L_N_XS(v0, v1) -> null_COND_TAKE_L_N_XS [0] PLUS#2(v0, v1) -> null_PLUS#2 [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] ZIPWITH_L_F_XS_YS#1(v0, v1, v2, v3) -> null_ZIPWITH_L_F_XS_YS#1 [0] The TRS has the following type information: COND_TAKE_L_N_XS :: ConsL:null_zipwith_l_f_xs_ys#1:null_cond_zipwith_l_f_xs_ys:null_cond_zipwith_l_f_xs_ys_1:null_fibs_2#1 -> S:0:null_plus#2 -> c3:c2:null_COND_TAKE_L_N_XS ConsL :: S:0:null_plus#2 -> zipwith_l_f_xs_ys:fibs:fibs_2:null_zipwith_l#3 -> ConsL:null_zipwith_l_f_xs_ys#1:null_cond_zipwith_l_f_xs_ys:null_cond_zipwith_l_f_xs_ys_1:null_fibs_2#1 zipwith_l_f_xs_ys :: plus -> zipwith_l_f_xs_ys:fibs:fibs_2:null_zipwith_l#3 -> zipwith_l_f_xs_ys:fibs:fibs_2:null_zipwith_l#3 -> zipwith_l_f_xs_ys:fibs:fibs_2:null_zipwith_l#3 S :: S:0:null_plus#2 -> S:0:null_plus#2 c3 :: c3:c2:null_COND_TAKE_L_N_XS -> c10:c12:c11:null_ZIPWITH_L_F_XS_YS#1 -> c3:c2:null_COND_TAKE_L_N_XS zipwith_l_f_xs_ys#1 :: plus -> zipwith_l_f_xs_ys:fibs:fibs_2:null_zipwith_l#3 -> zipwith_l_f_xs_ys:fibs:fibs_2:null_zipwith_l#3 -> bot[0]:bot[6]:bot[7] -> ConsL:null_zipwith_l_f_xs_ys#1:null_cond_zipwith_l_f_xs_ys:null_cond_zipwith_l_f_xs_ys_1:null_fibs_2#1 bot[0] :: bot[0]:bot[6]:bot[7] ZIPWITH_L_F_XS_YS#1 :: plus -> zipwith_l_f_xs_ys:fibs:fibs_2:null_zipwith_l#3 -> zipwith_l_f_xs_ys:fibs:fibs_2:null_zipwith_l#3 -> bot[0]:bot[6]:bot[7] -> c10:c12:c11:null_ZIPWITH_L_F_XS_YS#1 PLUS#2 :: S:0:null_plus#2 -> S:0:null_plus#2 -> c5:null_PLUS#2 c5 :: c5:null_PLUS#2 -> c5:null_PLUS#2 COND_ZIPWITH_L_F_XS_YS_1 :: ConsL:null_zipwith_l_f_xs_ys#1:null_cond_zipwith_l_f_xs_ys:null_cond_zipwith_l_f_xs_ys_1:null_fibs_2#1 -> S:0:null_plus#2 -> zipwith_l_f_xs_ys:fibs:fibs_2:null_zipwith_l#3 -> c6:null_COND_ZIPWITH_L_F_XS_YS_1 c6 :: c5:null_PLUS#2 -> c6:null_COND_ZIPWITH_L_F_XS_YS_1 COND_ZIPWITH_L_F_XS_YS :: ConsL:null_zipwith_l_f_xs_ys#1:null_cond_zipwith_l_f_xs_ys:null_cond_zipwith_l_f_xs_ys_1:null_fibs_2#1 -> zipwith_l_f_xs_ys:fibs:fibs_2:null_zipwith_l#3 -> c8:c9:null_COND_ZIPWITH_L_F_XS_YS c8 :: c6:null_COND_ZIPWITH_L_F_XS_YS_1 -> c10:c12:c11:null_ZIPWITH_L_F_XS_YS#1 -> c8:c9:null_COND_ZIPWITH_L_F_XS_YS bot[6] :: bot[0]:bot[6]:bot[7] plus :: plus fibs :: zipwith_l_f_xs_ys:fibs:fibs_2:null_zipwith_l#3 c10 :: c8:c9:null_COND_ZIPWITH_L_F_XS_YS -> c10:c12:c11:null_ZIPWITH_L_F_XS_YS#1 0 :: S:0:null_plus#2 fibs_2 :: zipwith_l -> plus -> tail_l -> zipwith_l_f_xs_ys:fibs:fibs_2:null_zipwith_l#3 zipwith_l :: zipwith_l tail_l :: tail_l c12 :: c8:c9:null_COND_ZIPWITH_L_F_XS_YS -> c10:c12:c11:null_ZIPWITH_L_F_XS_YS#1 -> c10:c12:c11:null_ZIPWITH_L_F_XS_YS#1 bot[7] :: bot[0]:bot[6]:bot[7] c2 :: c3:c2:null_COND_TAKE_L_N_XS -> c3:c2:null_COND_TAKE_L_N_XS fibs_2#1 :: zipwith_l -> plus -> tail_l -> bot[0]:bot[6]:bot[7] -> ConsL:null_zipwith_l_f_xs_ys#1:null_cond_zipwith_l_f_xs_ys:null_cond_zipwith_l_f_xs_ys_1:null_fibs_2#1 c9 :: c6:null_COND_ZIPWITH_L_F_XS_YS_1 -> c8:c9:null_COND_ZIPWITH_L_F_XS_YS c11 :: c8:c9:null_COND_ZIPWITH_L_F_XS_YS -> c10:c12:c11:null_ZIPWITH_L_F_XS_YS#1 cond_zipwith_l_f_xs_ys :: ConsL:null_zipwith_l_f_xs_ys#1:null_cond_zipwith_l_f_xs_ys:null_cond_zipwith_l_f_xs_ys_1:null_fibs_2#1 -> zipwith_l_f_xs_ys:fibs:fibs_2:null_zipwith_l#3 -> ConsL:null_zipwith_l_f_xs_ys#1:null_cond_zipwith_l_f_xs_ys:null_cond_zipwith_l_f_xs_ys_1:null_fibs_2#1 cond_zipwith_l_f_xs_ys_1 :: ConsL:null_zipwith_l_f_xs_ys#1:null_cond_zipwith_l_f_xs_ys:null_cond_zipwith_l_f_xs_ys_1:null_fibs_2#1 -> S:0:null_plus#2 -> zipwith_l_f_xs_ys:fibs:fibs_2:null_zipwith_l#3 -> ConsL:null_zipwith_l_f_xs_ys#1:null_cond_zipwith_l_f_xs_ys:null_cond_zipwith_l_f_xs_ys_1:null_fibs_2#1 plus#2 :: S:0:null_plus#2 -> S:0:null_plus#2 -> S:0:null_plus#2 zipwith_l#3 :: zipwith_l_f_xs_ys:fibs:fibs_2:null_zipwith_l#3 -> zipwith_l_f_xs_ys:fibs:fibs_2:null_zipwith_l#3 -> zipwith_l_f_xs_ys:fibs:fibs_2:null_zipwith_l#3 null_zipwith_l_f_xs_ys#1 :: ConsL:null_zipwith_l_f_xs_ys#1:null_cond_zipwith_l_f_xs_ys:null_cond_zipwith_l_f_xs_ys_1:null_fibs_2#1 null_cond_zipwith_l_f_xs_ys :: ConsL:null_zipwith_l_f_xs_ys#1:null_cond_zipwith_l_f_xs_ys:null_cond_zipwith_l_f_xs_ys_1:null_fibs_2#1 null_cond_zipwith_l_f_xs_ys_1 :: ConsL:null_zipwith_l_f_xs_ys#1:null_cond_zipwith_l_f_xs_ys:null_cond_zipwith_l_f_xs_ys_1:null_fibs_2#1 null_fibs_2#1 :: ConsL:null_zipwith_l_f_xs_ys#1:null_cond_zipwith_l_f_xs_ys:null_cond_zipwith_l_f_xs_ys_1:null_fibs_2#1 null_zipwith_l#3 :: zipwith_l_f_xs_ys:fibs:fibs_2:null_zipwith_l#3 null_plus#2 :: S:0:null_plus#2 null_COND_TAKE_L_N_XS :: c3:c2:null_COND_TAKE_L_N_XS null_PLUS#2 :: c5:null_PLUS#2 null_COND_ZIPWITH_L_F_XS_YS_1 :: c6:null_COND_ZIPWITH_L_F_XS_YS_1 null_COND_ZIPWITH_L_F_XS_YS :: c8:c9:null_COND_ZIPWITH_L_F_XS_YS null_ZIPWITH_L_F_XS_YS#1 :: c10:c12:c11:null_ZIPWITH_L_F_XS_YS#1 Rewrite Strategy: INNERMOST ---------------------------------------- (43) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID)) Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction. The constant constructors are abstracted as follows: bot[0] => 0 bot[6] => 1 plus => 0 fibs => 0 0 => 0 zipwith_l => 0 tail_l => 0 bot[7] => 2 null_zipwith_l_f_xs_ys#1 => 0 null_cond_zipwith_l_f_xs_ys => 0 null_cond_zipwith_l_f_xs_ys_1 => 0 null_fibs_2#1 => 0 null_zipwith_l#3 => 0 null_plus#2 => 0 null_COND_TAKE_L_N_XS => 0 null_PLUS#2 => 0 null_COND_ZIPWITH_L_F_XS_YS_1 => 0 null_COND_ZIPWITH_L_F_XS_YS => 0 null_ZIPWITH_L_F_XS_YS#1 => 0 ---------------------------------------- (44) Obligation: Complexity RNTS consisting of the following rules: 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 + COND_TAKE_L_N_XS(fibs_2#1(z1, z2, z3, 0), z4) :|: z' = 1 + z4, z1 >= 0, z = 1 + z0 + (1 + z1 + z2 + z3), z0 >= 0, z4 >= 0, z2 >= 0, z3 >= 0 COND_TAKE_L_N_XS(z, z') -{ 1 }-> 1 + COND_TAKE_L_N_XS(zipwith_l_f_xs_ys#1(z1, z2, z3, 0), z4) + ZIPWITH_L_F_XS_YS#1(z1, z2, z3, 0) :|: z' = 1 + z4, z1 >= 0, z = 1 + z0 + (1 + z1 + z2 + z3), z0 >= 0, z4 >= 0, z2 >= 0, z3 >= 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(z, z') -{ 1 }-> 1 + COND_ZIPWITH_L_F_XS_YS_1(fibs_2#1(z2, z3, z4, 1), z0, z1) :|: z' = 1 + z2 + z3 + z4, z1 >= 0, z0 >= 0, z4 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0 COND_ZIPWITH_L_F_XS_YS(z, z') -{ 1 }-> 1 + COND_ZIPWITH_L_F_XS_YS_1(zipwith_l_f_xs_ys#1(z2, z3, z4, 1), z0, z1) + ZIPWITH_L_F_XS_YS#1(z2, z3, z4, 1) :|: z' = 1 + z2 + z3 + z4, z1 >= 0, z0 >= 0, z4 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0 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(z2, z0) :|: z1 >= 0, z' = z2, z0 >= 0, z'' = z3, z = 1 + z0 + z1, z2 >= 0, z3 >= 0 PLUS#2(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 PLUS#2(z, z') -{ 1 }-> 1 + PLUS#2(z0, z1) :|: z1 >= 0, z = 1 + z0, z' = z1, z0 >= 0 ZIPWITH_L_F_XS_YS#1(z, z', z'', z5) -{ 0 }-> 0 :|: z5 = v3, v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0, v3 >= 0 ZIPWITH_L_F_XS_YS#1(z, z', z'', z5) -{ 1 }-> 1 + COND_ZIPWITH_L_F_XS_YS(fibs_2#1(z0, z1, z2, 2), z3) :|: z1 >= 0, z' = 1 + z0 + z1 + z2, z5 = z4, z0 >= 0, z'' = z3, z4 >= 0, z = 0, z2 >= 0, z3 >= 0 ZIPWITH_L_F_XS_YS#1(z, z', z'', z5) -{ 1 }-> 1 + COND_ZIPWITH_L_F_XS_YS(1 + 0 + (1 + 0 + 0 + 0), z0) :|: z1 >= 0, z'' = z0, z0 >= 0, z = 0, z' = 0, z5 = z1 ZIPWITH_L_F_XS_YS#1(z, z', z'', z5) -{ 1 }-> 1 + COND_ZIPWITH_L_F_XS_YS(zipwith_l_f_xs_ys#1(z0, z1, z2, 2), z3) + ZIPWITH_L_F_XS_YS#1(z0, z1, z2, 2) :|: z1 >= 0, z' = 1 + z0 + z1 + z2, z5 = z4, z0 >= 0, z'' = z3, z4 >= 0, z = 0, z2 >= 0, z3 >= 0 cond_zipwith_l_f_xs_ys(z, z') -{ 0 }-> cond_zipwith_l_f_xs_ys_1(zipwith_l_f_xs_ys#1(z2, z3, z4, 1), z0, z1) :|: z' = 1 + z2 + z3 + z4, z1 >= 0, z0 >= 0, z4 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0 cond_zipwith_l_f_xs_ys(z, z') -{ 0 }-> cond_zipwith_l_f_xs_ys_1(fibs_2#1(z2, z3, z4, 1), z0, z1) :|: z' = 1 + z2 + z3 + z4, z1 >= 0, z0 >= 0, z4 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 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'') -{ 0 }-> 1 + plus#2(z2, z0) + zipwith_l#3(z3, z1) :|: z1 >= 0, z' = z2, z0 >= 0, z'' = z3, z = 1 + z0 + z1, z2 >= 0, z3 >= 0 fibs_2#1(z, z', z'', z5) -{ 0 }-> 0 :|: z5 = v3, v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0, v3 >= 0 fibs_2#1(z, z', z'', z5) -{ 0 }-> 1 + (1 + 0) + zipwith_l#3(0, 1 + 0 + 0 + 0) :|: z'' = 0, z0 >= 0, z = 0, z5 = z0, z' = 0 plus#2(z, z') -{ 0 }-> z0 :|: z0 >= 0, z = 0, z' = z0 plus#2(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 plus#2(z, z') -{ 0 }-> 1 + plus#2(z0, z1) :|: z1 >= 0, z = 1 + z0, z' = z1, z0 >= 0 zipwith_l#3(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 zipwith_l#3(z, z') -{ 0 }-> 1 + 0 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 zipwith_l_f_xs_ys#1(z, z', z'', z5) -{ 0 }-> cond_zipwith_l_f_xs_ys(zipwith_l_f_xs_ys#1(z0, z1, z2, 2), z3) :|: z1 >= 0, z' = 1 + z0 + z1 + z2, z5 = z4, z0 >= 0, z'' = z3, z4 >= 0, z = 0, z2 >= 0, z3 >= 0 zipwith_l_f_xs_ys#1(z, z', z'', z5) -{ 0 }-> cond_zipwith_l_f_xs_ys(fibs_2#1(z0, z1, z2, 2), z3) :|: z1 >= 0, z' = 1 + z0 + z1 + z2, z5 = z4, z0 >= 0, z'' = z3, z4 >= 0, z = 0, z2 >= 0, z3 >= 0 zipwith_l_f_xs_ys#1(z, z', z'', z5) -{ 0 }-> cond_zipwith_l_f_xs_ys(1 + 0 + (1 + 0 + 0 + 0), z0) :|: z1 >= 0, z'' = z0, z0 >= 0, z = 0, z' = 0, z5 = z1 zipwith_l_f_xs_ys#1(z, z', z'', z5) -{ 0 }-> 0 :|: z5 = v3, v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0, v3 >= 0 Only complete derivations are relevant for the runtime complexity. ---------------------------------------- (45) 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 ---------------------------------------- (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: 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 ---------------------------------------- (47) 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])) ---------------------------------------- (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)) 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 ---------------------------------------- (49) 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])) ---------------------------------------- (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)) 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 ---------------------------------------- (51) 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])) ---------------------------------------- (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_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 ---------------------------------------- (53) 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)) ---------------------------------------- (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(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 ---------------------------------------- (55) 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)) ---------------------------------------- (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, 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 ---------------------------------------- (57) 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)) ---------------------------------------- (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)) 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 ---------------------------------------- (59) 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])) ---------------------------------------- (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)) 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 ---------------------------------------- (61) 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])) ---------------------------------------- (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, 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 ---------------------------------------- (63) 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])) ---------------------------------------- (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), 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 ---------------------------------------- (65) 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])) ---------------------------------------- (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)) 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 ---------------------------------------- (67) 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])) ---------------------------------------- (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_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 ---------------------------------------- (69) 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])) ---------------------------------------- (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)) 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 ---------------------------------------- (71) 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])) ---------------------------------------- (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)) 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 ---------------------------------------- (73) 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])) ---------------------------------------- (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: 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 ---------------------------------------- (75) 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])) ---------------------------------------- (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: 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 ---------------------------------------- (77) 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)) ---------------------------------------- (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: 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 ---------------------------------------- (79) 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)) ---------------------------------------- (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: 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 ---------------------------------------- (81) 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)) ---------------------------------------- (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: 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 ---------------------------------------- (83) 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])) ---------------------------------------- (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: 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 ---------------------------------------- (85) 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)) ---------------------------------------- (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: 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_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])) 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: 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(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)) 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: PLUS#2_2, 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 Compound Symbols: c5_1, c6_1, c3_2, c3_1, c8_2, c8_1, c12_2, c12_1, c2_1, c9_1, c11_1, c10_1 ---------------------------------------- (87) 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: 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_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])) 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 ---------------------------------------- (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: 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_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])) 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: 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(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)) 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: PLUS#2_2, 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 Compound Symbols: c5_1, c6_1, c3_2, c3_1, c8_2, c8_1, c12_2, c12_1, c2_1, c9_1, c11_1, c10_1 ---------------------------------------- (89) 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])) ---------------------------------------- (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: 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_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])) 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)) 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)) 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)) 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)) 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)) 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: PLUS#2_2, 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 Compound Symbols: c5_1, c6_1, c3_2, c3_1, c8_2, c8_1, c12_2, c12_1, c2_1, c9_1, c11_1, c10_1 ---------------------------------------- (91) 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)) ---------------------------------------- (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, 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])) 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)) 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)) 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)) 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)) 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)) 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, c10_1, c5_1 ---------------------------------------- (93) 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])) ---------------------------------------- (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, 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])) 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)) 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, 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)) 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)) 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, 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, c10_1, c5_1 ---------------------------------------- (95) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID)) Split RHS of tuples not part of any SCC ---------------------------------------- (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, 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])) 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)) 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, 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)) 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)) 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, 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, c10_1, c5_1, c_1 ---------------------------------------- (97) 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])) 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)) 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, 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)) = [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(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 ---------------------------------------- (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, 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])) 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)) 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, 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)) 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)) 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, 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, c10_1, c5_1, c_1 ---------------------------------------- (99) 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)) ---------------------------------------- (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_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])) 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)) 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, 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])) 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])) 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)) 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)) 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, 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])) 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])) 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, PLUS#2_2, COND_ZIPWITH_L_F_XS_YS_1_3 Compound Symbols: c3_2, c3_1, c8_2, c8_1, c12_2, c12_1, c2_1, c9_1, c11_1, c10_1, c5_1, c_1, c6_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, 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])) ---------------------------------------- (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_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])) 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)) 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, 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])) 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, 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(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)) 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)) 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, 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])) 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, 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_TAKE_L_N_XS_2, COND_ZIPWITH_L_F_XS_YS_2, ZIPWITH_L_F_XS_YS#1_4, PLUS#2_2, COND_ZIPWITH_L_F_XS_YS_1_3 Compound Symbols: c3_2, c3_1, c8_2, c8_1, c12_1, c12_2, c2_1, c9_1, c11_1, c10_1, c5_1, c_1, c6_1 ---------------------------------------- (103) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID)) Split RHS of tuples not part of any SCC ---------------------------------------- (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_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])) 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)) 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, 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])) 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, 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(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)) 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)) 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, 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])) 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, 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_TAKE_L_N_XS_2, COND_ZIPWITH_L_F_XS_YS_2, ZIPWITH_L_F_XS_YS#1_4, PLUS#2_2, COND_ZIPWITH_L_F_XS_YS_1_3 Compound Symbols: c3_2, c3_1, c8_2, c8_1, c12_1, c12_2, c2_1, c9_1, c11_1, c10_1, c5_1, c_1, c6_1, c1_1 ---------------------------------------- (105) 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_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])) 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)) 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, 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])) 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, 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)) = 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 ---------------------------------------- (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_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])) 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)) 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, 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])) 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, 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(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)) 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)) 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, 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])) 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, 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_TAKE_L_N_XS_2, COND_ZIPWITH_L_F_XS_YS_2, ZIPWITH_L_F_XS_YS#1_4, PLUS#2_2, COND_ZIPWITH_L_F_XS_YS_1_3 Compound Symbols: c3_2, c3_1, c8_2, c8_1, c12_1, c12_2, c2_1, c9_1, c11_1, c10_1, c5_1, c_1, c6_1, c1_1 ---------------------------------------- (107) 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])) ---------------------------------------- (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_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])) 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)) 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, 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])) 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, 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(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)) 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)) 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, 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])) 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, 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_TAKE_L_N_XS_2, COND_ZIPWITH_L_F_XS_YS_2, ZIPWITH_L_F_XS_YS#1_4, PLUS#2_2, COND_ZIPWITH_L_F_XS_YS_1_3 Compound Symbols: c3_2, c3_1, c8_2, c8_1, c12_2, c12_1, c2_1, c9_1, c11_1, c10_1, c5_1, c_1, c6_1, c1_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, 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_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])) 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)) 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, 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])) 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, 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_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 ---------------------------------------- (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_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])) 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)) 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, 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])) 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, 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(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)) 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)) 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, 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])) 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, 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_TAKE_L_N_XS_2, COND_ZIPWITH_L_F_XS_YS_2, ZIPWITH_L_F_XS_YS#1_4, PLUS#2_2, COND_ZIPWITH_L_F_XS_YS_1_3 Compound Symbols: c3_2, c3_1, c8_2, c8_1, c12_2, c12_1, c2_1, c9_1, c11_1, c10_1, c5_1, c_1, c6_1, c1_1 ---------------------------------------- (111) 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])) ---------------------------------------- (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_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])) 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)) 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, 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])) 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, 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(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)) 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)) 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, 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])) 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, 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_TAKE_L_N_XS_2, COND_ZIPWITH_L_F_XS_YS_2, ZIPWITH_L_F_XS_YS#1_4, PLUS#2_2, COND_ZIPWITH_L_F_XS_YS_1_3 Compound Symbols: c3_2, c3_1, c8_2, c8_1, c12_1, c12_2, c2_1, c9_1, c11_1, c10_1, c5_1, c_1, c6_1, c1_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_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])) 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)) 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, 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])) 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, 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(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)) 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)) 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, 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])) 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, 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_TAKE_L_N_XS_2, COND_ZIPWITH_L_F_XS_YS_2, ZIPWITH_L_F_XS_YS#1_4, PLUS#2_2, COND_ZIPWITH_L_F_XS_YS_1_3 Compound Symbols: c3_2, c3_1, c8_2, c8_1, c12_1, c12_2, c2_1, c9_1, c11_1, c10_1, c5_1, c_1, c6_1, c1_1, c4_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, 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_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])) 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)) 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, 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])) 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, 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)) = [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(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) = [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 ---------------------------------------- (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_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])) 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)) 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, 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])) 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, 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(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)) 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)) 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, 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])) 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, 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_TAKE_L_N_XS_2, COND_ZIPWITH_L_F_XS_YS_2, ZIPWITH_L_F_XS_YS#1_4, PLUS#2_2, COND_ZIPWITH_L_F_XS_YS_1_3 Compound Symbols: c3_2, c3_1, c8_2, c8_1, c12_1, c12_2, c2_1, c9_1, c11_1, c10_1, c5_1, c_1, c6_1, c1_1, c4_1 ---------------------------------------- (117) 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])) ---------------------------------------- (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_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])) 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)) 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, 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])) 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, 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(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)) 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)) 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, 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])) 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, 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_TAKE_L_N_XS_2, COND_ZIPWITH_L_F_XS_YS_2, ZIPWITH_L_F_XS_YS#1_4, PLUS#2_2, COND_ZIPWITH_L_F_XS_YS_1_3 Compound Symbols: c3_2, c3_1, c8_2, c8_1, c12_2, c12_1, c2_1, c9_1, c11_1, c10_1, c5_1, c_1, c6_1, c1_1, c4_1 ---------------------------------------- (119) 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: 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#3(z0, z1) -> zipwith_l_f_xs_ys(plus, z0, z1) cond_zipwith_l_f_xs_ys_1(ConsL(z0, z1), z2, z3) -> ConsL(plus#2(z2, z0), zipwith_l#3(z3, 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) 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) 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) 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_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) And the 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])) 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])) 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)) 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, 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])) 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, 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_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)) = x_2 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)) = x_1 POL(cond_zipwith_l_f_xs_ys_1(x_1, x_2, x_3)) = x_3 POL(fibs) = [1] POL(fibs_2(x_1, x_2, x_3)) = x_1 POL(fibs_2#1(x_1, x_2, x_3, x_4)) = x_1 POL(plus) = 0 POL(plus#2(x_1, x_2)) = [1] + x_1 + x_2 POL(tail_l) = 0 POL(zipwith_l) = [1] POL(zipwith_l#3(x_1, x_2)) = x_1 POL(zipwith_l_f_xs_ys(x_1, x_2, x_3)) = x_2 POL(zipwith_l_f_xs_ys#1(x_1, x_2, x_3, x_4)) = x_2 ---------------------------------------- (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_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])) 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)) 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, 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])) 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, 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(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)) 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)) 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, 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])) 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, 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_TAKE_L_N_XS_2, COND_ZIPWITH_L_F_XS_YS_2, ZIPWITH_L_F_XS_YS#1_4, PLUS#2_2, COND_ZIPWITH_L_F_XS_YS_1_3 Compound Symbols: c3_2, c3_1, c8_2, c8_1, c12_2, c12_1, c2_1, c9_1, c11_1, c10_1, c5_1, c_1, c6_1, c1_1, c4_1 ---------------------------------------- (121) 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])) ---------------------------------------- (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_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])) 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)) 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, 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])) 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, 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(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)) 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)) 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, 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])) 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, 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_TAKE_L_N_XS_2, COND_ZIPWITH_L_F_XS_YS_2, ZIPWITH_L_F_XS_YS#1_4, PLUS#2_2, COND_ZIPWITH_L_F_XS_YS_1_3 Compound Symbols: c3_2, c3_1, c8_2, c8_1, c12_2, c12_1, c2_1, c9_1, c11_1, c10_1, c5_1, c_1, c6_1, c1_1, c4_1 ---------------------------------------- (123) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID)) Split RHS of tuples not part of any SCC ---------------------------------------- (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_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])) 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)) 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, 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])) 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, 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(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)) 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)) 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, 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])) 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, 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_TAKE_L_N_XS_2, COND_ZIPWITH_L_F_XS_YS_2, ZIPWITH_L_F_XS_YS#1_4, PLUS#2_2, COND_ZIPWITH_L_F_XS_YS_1_3 Compound Symbols: c3_2, c3_1, c8_2, c8_1, c12_2, c12_1, c2_1, c9_1, c11_1, c10_1, c5_1, c_1, c6_1, c1_1, c4_1, c7_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(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_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])) 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)) 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, 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])) 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, 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)) = 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 ---------------------------------------- (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_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])) 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)) 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, 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])) 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, 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(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)) 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)) 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, 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])) 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, 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_TAKE_L_N_XS_2, COND_ZIPWITH_L_F_XS_YS_2, ZIPWITH_L_F_XS_YS#1_4, PLUS#2_2, COND_ZIPWITH_L_F_XS_YS_1_3 Compound Symbols: c3_2, c3_1, c8_2, c8_1, c12_2, c12_1, c2_1, c9_1, c11_1, c10_1, c5_1, c_1, c6_1, c1_1, c4_1, c7_1 ---------------------------------------- (127) 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])) ---------------------------------------- (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_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])) 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)) 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, 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])) 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, 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(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)) 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)) 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, 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])) 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, 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_TAKE_L_N_XS_2, COND_ZIPWITH_L_F_XS_YS_2, ZIPWITH_L_F_XS_YS#1_4, PLUS#2_2, COND_ZIPWITH_L_F_XS_YS_1_3 Compound Symbols: c3_2, c3_1, c8_2, c8_1, c12_2, c12_1, c2_1, c9_1, c11_1, c10_1, c5_1, c_1, c6_1, c1_1, c4_1, c7_1 ---------------------------------------- (129) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID)) Split RHS of tuples not part of any SCC ---------------------------------------- (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_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])) 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)) 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, 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])) 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, 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(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)) 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)) 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, 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])) 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, 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_TAKE_L_N_XS_2, COND_ZIPWITH_L_F_XS_YS_2, ZIPWITH_L_F_XS_YS#1_4, PLUS#2_2, COND_ZIPWITH_L_F_XS_YS_1_3 Compound Symbols: c3_2, c3_1, c8_2, c8_1, c12_2, c12_1, c2_1, c9_1, c11_1, c10_1, c5_1, c_1, c6_1, c1_1, c4_1, c7_1, c13_1 ---------------------------------------- (131) 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_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])) 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)) 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, 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])) 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, 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)) = 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 ---------------------------------------- (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])) ZIPWITH_L_F_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])) 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)) 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, 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])) 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, 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(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)) 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)) 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, 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])) 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, 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_TAKE_L_N_XS_2, COND_ZIPWITH_L_F_XS_YS_2, ZIPWITH_L_F_XS_YS#1_4, PLUS#2_2, COND_ZIPWITH_L_F_XS_YS_1_3 Compound Symbols: c3_2, c3_1, c8_2, c8_1, c12_2, c12_1, c2_1, c9_1, c11_1, c10_1, c5_1, c_1, c6_1, c1_1, c4_1, c7_1, c13_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])) ZIPWITH_L_F_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])) 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)) 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, 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])) 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, 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])) 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])) ZIPWITH_L_F_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)) 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)) 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, 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])) 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, 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_TAKE_L_N_XS_2, COND_ZIPWITH_L_F_XS_YS_2, ZIPWITH_L_F_XS_YS#1_4, PLUS#2_2, COND_ZIPWITH_L_F_XS_YS_1_3 Compound Symbols: c3_2, c3_1, c8_2, c8_1, c12_2, c12_1, c2_1, c9_1, c11_1, c10_1, c5_1, c_1, c6_1, c1_1, c4_1, c7_1, c13_1 ---------------------------------------- (135) 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])) ---------------------------------------- (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])) 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])) 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)) 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, 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])) 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, 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])) 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, 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(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)) 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)) 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, 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])) 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, 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_TAKE_L_N_XS_2, COND_ZIPWITH_L_F_XS_YS_2, ZIPWITH_L_F_XS_YS#1_4, PLUS#2_2, COND_ZIPWITH_L_F_XS_YS_1_3 Compound Symbols: c3_2, c3_1, c8_2, c8_1, c12_1, c2_1, c9_1, c11_1, c10_1, c5_1, c12_2, c_1, c6_1, c1_1, c4_1, c7_1, c13_1 ---------------------------------------- (137) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID)) Split RHS of tuples not part of any SCC ---------------------------------------- (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_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])) 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)) 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, 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])) 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, 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])) 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, 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(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)) 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)) 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, 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])) 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, 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_TAKE_L_N_XS_2, COND_ZIPWITH_L_F_XS_YS_2, ZIPWITH_L_F_XS_YS#1_4, PLUS#2_2, COND_ZIPWITH_L_F_XS_YS_1_3 Compound Symbols: c3_2, c3_1, c8_2, c8_1, c12_1, c2_1, c9_1, c11_1, c10_1, c5_1, c12_2, c_1, c6_1, c1_1, c4_1, c7_1, c13_1, c14_1 ---------------------------------------- (139) 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_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])) 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])) 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)) 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, 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])) 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, 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])) 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, 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 ---------------------------------------- (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_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])) 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)) 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, 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])) 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, 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])) 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, 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(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)) 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)) 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, 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])) 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, 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_TAKE_L_N_XS_2, COND_ZIPWITH_L_F_XS_YS_2, ZIPWITH_L_F_XS_YS#1_4, PLUS#2_2, COND_ZIPWITH_L_F_XS_YS_1_3 Compound Symbols: c3_2, c3_1, c8_2, c8_1, c12_1, c2_1, c9_1, c11_1, c10_1, c5_1, c12_2, c_1, c6_1, c1_1, c4_1, c7_1, c13_1, c14_1 ---------------------------------------- (141) 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])) ---------------------------------------- (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_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])) 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)) 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, 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])) 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, 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])) 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, 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(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)) 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)) 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, 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])) 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, 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_TAKE_L_N_XS_2, COND_ZIPWITH_L_F_XS_YS_2, ZIPWITH_L_F_XS_YS#1_4, PLUS#2_2, COND_ZIPWITH_L_F_XS_YS_1_3 Compound Symbols: c3_2, c3_1, c8_2, c8_1, c2_1, c9_1, c11_1, c10_1, c5_1, c12_2, c_1, c6_1, c1_1, c12_1, c4_1, c7_1, c13_1, c14_1 ---------------------------------------- (143) 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_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)) 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])) 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)) 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, 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])) 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, 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])) 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, 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 ---------------------------------------- (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_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])) 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)) 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, 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])) 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, 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])) 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, 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(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)) 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)) 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, 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])) 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, 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_TAKE_L_N_XS_2, COND_ZIPWITH_L_F_XS_YS_2, ZIPWITH_L_F_XS_YS#1_4, PLUS#2_2, COND_ZIPWITH_L_F_XS_YS_1_3 Compound Symbols: c3_2, c3_1, c8_2, c8_1, c2_1, c9_1, c11_1, c10_1, c5_1, c12_2, c_1, c6_1, c1_1, c12_1, c4_1, c7_1, c13_1, c14_1 ---------------------------------------- (145) 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), 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), x1, 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))), x1)) 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)) ---------------------------------------- (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_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])) 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)) 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, 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])) 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, 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])) 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, 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), 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), x1, 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))), x1)) 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(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, 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)) 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, 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])) 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, 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), x1, 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))), x1)) 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_TAKE_L_N_XS_2, COND_ZIPWITH_L_F_XS_YS_2, ZIPWITH_L_F_XS_YS#1_4, PLUS#2_2, COND_ZIPWITH_L_F_XS_YS_1_3 Compound Symbols: c3_2, c3_1, c8_2, c8_1, c2_1, c9_1, c10_1, c5_1, c12_2, c_1, c6_1, c1_1, c12_1, c4_1, c7_1, c13_1, c14_1, c11_1 ---------------------------------------- (147) 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), x1, 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))), x1)) We considered the (Usable) Rules:none And the 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])) 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)) 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, 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])) 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, 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])) 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, 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), 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), x1, 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))), x1)) 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)) = 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 ---------------------------------------- (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_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])) 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)) 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, 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])) 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, 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])) 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, 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), 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), x1, 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))), x1)) 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(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, 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)) 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, 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])) 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, 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), x1, 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))), 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_TAKE_L_N_XS_2, COND_ZIPWITH_L_F_XS_YS_2, ZIPWITH_L_F_XS_YS#1_4, PLUS#2_2, COND_ZIPWITH_L_F_XS_YS_1_3 Compound Symbols: c3_2, c3_1, c8_2, c8_1, c2_1, c9_1, c10_1, c5_1, c12_2, c_1, c6_1, c1_1, c12_1, c4_1, c7_1, c13_1, c14_1, c11_1 ---------------------------------------- (149) 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])) ---------------------------------------- (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, 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])) 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)) 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, 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])) 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, 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])) 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, 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), 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), x1, 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))), x1)) 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_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)) 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)) 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, 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])) 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, 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), x1, 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))), 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_TAKE_L_N_XS_2, COND_ZIPWITH_L_F_XS_YS_2, ZIPWITH_L_F_XS_YS#1_4, PLUS#2_2, COND_ZIPWITH_L_F_XS_YS_1_3 Compound Symbols: c3_2, c3_1, c8_2, c8_1, c2_1, c9_1, c10_1, c5_1, c12_2, c_1, c6_1, c1_1, c12_1, c4_1, c7_1, c13_1, c14_1, c11_1 ---------------------------------------- (151) 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])) ---------------------------------------- (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_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])) 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)) 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, 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])) 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, 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])) 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, 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), 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), x1, 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))), x1)) 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_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)) 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)) 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, 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])) 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, 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(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), x1, 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))), 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_TAKE_L_N_XS_2, COND_ZIPWITH_L_F_XS_YS_2, ZIPWITH_L_F_XS_YS#1_4, PLUS#2_2, COND_ZIPWITH_L_F_XS_YS_1_3 Compound Symbols: c3_2, c3_1, c8_2, c8_1, c2_1, c9_1, c10_1, c5_1, c12_2, c_1, c6_1, c1_1, c12_1, c4_1, c7_1, c13_1, c14_1, c11_1 ---------------------------------------- (153) 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(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(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])) ---------------------------------------- (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(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])) 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)) 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, 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])) 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, 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])) 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, 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), 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), x1, 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))), x1)) 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_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(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(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])) 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)) 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)) 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, 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])) 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, 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(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(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(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])) 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), x1, 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))), 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_TAKE_L_N_XS_2, COND_ZIPWITH_L_F_XS_YS_2, ZIPWITH_L_F_XS_YS#1_4, PLUS#2_2, COND_ZIPWITH_L_F_XS_YS_1_3 Compound Symbols: c3_2, c3_1, c8_2, c8_1, c2_1, c9_1, c10_1, c5_1, c12_2, c_1, c6_1, c1_1, c12_1, c4_1, c7_1, c13_1, c14_1, c11_1 ---------------------------------------- (155) 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))) ---------------------------------------- (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_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])) 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)) 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, 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])) 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, 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])) 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, 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), 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), x1, 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))), x1)) 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_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(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(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_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)) 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)) 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, 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])) 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, 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(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(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(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])) 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), x1, 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))), 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_TAKE_L_N_XS_2, COND_ZIPWITH_L_F_XS_YS_2, ZIPWITH_L_F_XS_YS#1_4, PLUS#2_2, COND_ZIPWITH_L_F_XS_YS_1_3 Compound Symbols: c3_2, c3_1, c8_2, c8_1, c9_1, c10_1, c5_1, c12_2, c_1, c6_1, c1_1, c12_1, c4_1, c7_1, c13_1, c14_1, c11_1, c2_1 ---------------------------------------- (157) 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)) ---------------------------------------- (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])) 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)) 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, 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])) 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, 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])) 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, 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), 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), x1, 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))), x1)) 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_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(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(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_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])) 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)) 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, 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])) 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, 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(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(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(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(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), x1, 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))), 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_TAKE_L_N_XS_2, COND_ZIPWITH_L_F_XS_YS_2, ZIPWITH_L_F_XS_YS#1_4, PLUS#2_2, COND_ZIPWITH_L_F_XS_YS_1_3 Compound Symbols: c3_2, c3_1, c8_2, c8_1, c10_1, c5_1, c12_2, c_1, c6_1, c1_1, c12_1, c4_1, c7_1, c13_1, c14_1, c11_1, c2_1, c9_1 ---------------------------------------- (159) 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(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, 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))) ---------------------------------------- (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, 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])) 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)) 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, 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])) 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, 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])) 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, 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), 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), x1, 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))), x1)) 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_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(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(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_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])) 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)) 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, 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])) 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, 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(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(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(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(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), x1, 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))), 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_TAKE_L_N_XS_2, COND_ZIPWITH_L_F_XS_YS_2, ZIPWITH_L_F_XS_YS#1_4, PLUS#2_2, COND_ZIPWITH_L_F_XS_YS_1_3 Compound Symbols: c3_2, c3_1, c8_2, c8_1, c10_1, c5_1, c12_2, c_1, c6_1, c1_1, c12_1, c4_1, c7_1, c13_1, c14_1, c11_1, c2_1, c9_1 ---------------------------------------- (161) 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, 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))) 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))) ---------------------------------------- (162) 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])) 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)) 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, 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])) 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, 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])) 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, 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), 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), x1, 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))), x1)) 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_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(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(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_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)) 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, 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))) 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))) 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])) 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)) 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, 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])) 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, 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(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(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(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(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, 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), x1, 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))), x1)) 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, 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))) 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))) 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, PLUS#2_2, COND_ZIPWITH_L_F_XS_YS_1_3 Compound Symbols: c3_2, c3_1, c8_2, c8_1, c10_1, c5_1, c12_2, c_1, c6_1, c1_1, c12_1, c4_1, c7_1, c13_1, c14_1, c11_1, c2_1, c9_1 ---------------------------------------- (163) 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, 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))) 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))) ---------------------------------------- (164) 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])) 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)) 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, 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])) 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, 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])) 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, 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), 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), x1, 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))), x1)) 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_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(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(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_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)) 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, 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))) 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))) 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])) 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)) 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, 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])) 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, 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(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(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(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(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, 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), x1, 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))), x1)) 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, 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))) 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))) 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, PLUS#2_2, COND_ZIPWITH_L_F_XS_YS_1_3 Compound Symbols: c3_2, c3_1, c8_2, c8_1, c10_1, c5_1, c12_2, c_1, c6_1, c1_1, c12_1, c4_1, c7_1, c13_1, c14_1, c11_1, c2_1, c9_1 ---------------------------------------- (165) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (166) 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])) 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)) 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, 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])) 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, 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])) 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, 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), 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), x1, 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))), x1)) 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_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(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(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_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)) 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, 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))) 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))) 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])) 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)) 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, 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])) 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, 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(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(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(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(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, 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), x1, 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))), x1)) 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, 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))) 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))) 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, PLUS#2_2, COND_ZIPWITH_L_F_XS_YS_1_3 Compound Symbols: c3_2, c3_1, c8_2, c8_1, c10_1, c5_1, c12_2, c_1, c6_1, c1_1, c12_1, c4_1, c7_1, c13_1, c14_1, c11_1, c2_1, c9_1 ---------------------------------------- (167) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace 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])) by COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(y0, y1, y2)))), S(z2)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(y0, y1, y2)), bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(plus, fibs, fibs_2(y0, y1, y2)))), S(z2)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, fibs, fibs_2(y0, y1, y2)), bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(plus, fibs, y0))), S(z2)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, fibs, y0), bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, y0), y1))), S(z2)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, y0), y1), bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), y3), y4))), S(z2)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), y3), y4), bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), y3), y4))), S(z2)) -> c3(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(y0, y1, y2), y3), y4), bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), y0))), S(z2)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), y0), bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(y0, y1, y2)), y3))), S(z2)) -> c3(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(y0, y1, y2)), y3), bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(y0, y1, y2)), y3))), S(z2)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(y0, y1, y2)), y3), bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), y0), y1))), S(z2)) -> c3(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), y0), y1), bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, y0), y1), y2))), S(z2)) -> c3(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, y0), y1), y2), bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), y3), y4), y5))), S(z2)) -> c3(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(y0, y1, y2), y3), y4), y5), bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(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(y0, y1, y2), y3), y4), y5))), S(z2)) -> c3(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(y0, y1, y2), y3), y4), y5), bot[0])) ---------------------------------------- (168) 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, 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])) 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)) 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, 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])) 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, 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])) 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, 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), 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), x1, 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))), x1)) 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_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(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(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_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)) 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, 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))) 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))) 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)) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(y0, y1, y2)))), S(z2)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(y0, y1, y2)), bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(plus, fibs, fibs_2(y0, y1, y2)))), S(z2)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, fibs, fibs_2(y0, y1, y2)), bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(plus, fibs, y0))), S(z2)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, fibs, y0), bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, y0), y1))), S(z2)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, y0), y1), bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), y3), y4))), S(z2)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), y3), y4), bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), y3), y4))), S(z2)) -> c3(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(y0, y1, y2), y3), y4), bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), y0))), S(z2)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), y0), bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(y0, y1, y2)), y3))), S(z2)) -> c3(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(y0, y1, y2)), y3), bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(y0, y1, y2)), y3))), S(z2)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(y0, y1, y2)), y3), bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), y0), y1))), S(z2)) -> c3(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), y0), y1), bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, y0), y1), y2))), S(z2)) -> c3(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, y0), y1), y2), bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), y3), y4), y5))), S(z2)) -> c3(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(y0, y1, y2), y3), y4), y5), bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(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(y0, y1, y2), y3), y4), y5))), S(z2)) -> c3(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(y0, y1, y2), y3), y4), y5), 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, 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])) 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)) 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, 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])) 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, 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(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(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(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(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, 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), x1, 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))), x1)) 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, 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))) 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))) 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, PLUS#2_2, COND_ZIPWITH_L_F_XS_YS_1_3 Compound Symbols: c3_2, c8_2, c8_1, c10_1, c5_1, c12_2, c_1, c6_1, c1_1, c12_1, c4_1, c7_1, c13_1, c3_1, c14_1, c11_1, c2_1, c9_1 ---------------------------------------- (169) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace 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))) 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[6]) -> 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[6]) -> 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[6]) -> 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[6]) -> 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[6]) -> 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[6]) -> 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[6]) -> 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[6]) -> 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[6]) -> 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, fibs_2(zipwith_l, plus, tail_l), y2), z2), bot[6]) -> 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))) 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[6]) -> 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[6]) -> 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[6]) -> 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))) ---------------------------------------- (170) 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, 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])) 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)) 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, 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])) 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, 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])) 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, 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), 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), x1, 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))), x1)) 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_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(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(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_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)) 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, 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))) 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))) 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)) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(y0, y1, y2)))), S(z2)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(y0, y1, y2)), bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(plus, fibs, fibs_2(y0, y1, y2)))), S(z2)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, fibs, fibs_2(y0, y1, y2)), bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(plus, fibs, y0))), S(z2)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, fibs, y0), bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, y0), y1))), S(z2)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, y0), y1), bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), y3), y4))), S(z2)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), y3), y4), bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), y3), y4))), S(z2)) -> c3(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(y0, y1, y2), y3), y4), bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), y0))), S(z2)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), y0), bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(y0, y1, y2)), y3))), S(z2)) -> c3(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(y0, y1, y2)), y3), bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(y0, y1, y2)), y3))), S(z2)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(y0, y1, y2)), y3), bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), y0), y1))), S(z2)) -> c3(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), y0), y1), bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, y0), y1), y2))), S(z2)) -> c3(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, y0), y1), y2), bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), y3), y4), y5))), S(z2)) -> c3(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(y0, y1, y2), y3), y4), y5), bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(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(y0, y1, y2), y3), y4), y5))), S(z2)) -> c3(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(y0, y1, y2), y3), y4), y5), bot[0])) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(y2, y3, y4)), bot[6]) -> 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[6]) -> 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[6]) -> 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[6]) -> 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[6]) -> 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[6]) -> 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[6]) -> 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[6]) -> 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[6]) -> 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, fibs_2(zipwith_l, plus, tail_l), y2), z2), bot[6]) -> 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))) 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[6]) -> 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[6]) -> 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[6]) -> 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))) 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])) 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)) 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, 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])) 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, 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(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(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(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(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)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(y2, y3, y4)), bot[6]) -> 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[6]) -> 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[6]) -> 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[6]) -> 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[6]) -> 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[6]) -> 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[6]) -> 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[6]) -> 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[6]) -> 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, fibs_2(zipwith_l, plus, tail_l), y2), z2), bot[6]) -> 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))) 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[6]) -> 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[6]) -> 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[6]) -> 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))) 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), x1, 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))), x1)) 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, 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))) 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))) 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, PLUS#2_2, COND_ZIPWITH_L_F_XS_YS_1_3 Compound Symbols: c3_2, c8_2, c8_1, c10_1, c5_1, c12_2, c_1, c6_1, c1_1, c12_1, c4_1, c7_1, c13_1, c3_1, c14_1, c11_1, c2_1, c9_1 ---------------------------------------- (171) 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])) ---------------------------------------- (172) 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, 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])) 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)) 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, 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])) 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, 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])) 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, 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), 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), x1, 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))), x1)) 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_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(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(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_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)) 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, 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))) 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))) 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)) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(y0, y1, y2)))), S(z2)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(y0, y1, y2)), bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(plus, fibs, fibs_2(y0, y1, y2)))), S(z2)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, fibs, fibs_2(y0, y1, y2)), bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(plus, fibs, y0))), S(z2)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, fibs, y0), bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, y0), y1))), S(z2)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, y0), y1), bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), y3), y4))), S(z2)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), y3), y4), bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(y0, y1, y2), y3), y4))), S(z2)) -> c3(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(y0, y1, y2), y3), y4), bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), y0))), S(z2)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), y0), bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(y0, y1, y2)), y3))), S(z2)) -> c3(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(y0, y1, y2)), y3), bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(y0, y1, y2)), y3))), S(z2)) -> c3(ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, fibs_2(y0, y1, y2)), y3), bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(zipwith_l, plus, tail_l), y0), y1))), S(z2)) -> c3(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), y0), y1), bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs, y0), y1), y2))), S(z2)) -> c3(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, y0), y1), y2), bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, zipwith_l_f_xs_ys(plus, fibs_2(y0, y1, y2), y3), y4), y5))), S(z2)) -> c3(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(y0, y1, y2), y3), y4), y5), bot[0])) COND_TAKE_L_N_XS(ConsL(z0, zipwith_l_f_xs_ys(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(y0, y1, y2), y3), y4), y5))), S(z2)) -> c3(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(y0, y1, y2), y3), y4), y5), bot[0])) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(y2, y3, y4)), bot[6]) -> 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[6]) -> 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[6]) -> 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[6]) -> 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[6]) -> 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[6]) -> 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[6]) -> 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[6]) -> 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[6]) -> 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, fibs_2(zipwith_l, plus, tail_l), y2), z2), bot[6]) -> 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))) 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[6]) -> 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[6]) -> 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[6]) -> 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, 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, 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])) 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)) 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, 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])) 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, 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(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(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(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(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)) ZIPWITH_L_F_XS_YS#1(plus, fibs, zipwith_l_f_xs_ys(plus, fibs, zipwith_l_f_xs_ys(y2, y3, y4)), bot[6]) -> 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[6]) -> 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[6]) -> 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[6]) -> 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[6]) -> 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[6]) -> 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[6]) -> 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[6]) -> 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[6]) -> 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, fibs_2(zipwith_l, plus, tail_l), y2), z2), bot[6]) -> 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))) 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[6]) -> 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[6]) -> 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[6]) -> 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, 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: 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), x1, 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))), x1)) 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, 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))) 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))) 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, PLUS#2_2, COND_ZIPWITH_L_F_XS_YS_1_3 Compound Symbols: c3_2, c8_2, c8_1, c10_1, c5_1, c12_2, c_1, c6_1, c1_1, c12_1, c4_1, c7_1, c13_1, c3_1, c14_1, c11_1, c2_1, c9_1 ---------------------------------------- (173) RelTrsToWeightedTrsProof (UPPER BOUND(ID)) Transformed relative TRS to weighted TRS ---------------------------------------- (174) 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 ---------------------------------------- (175) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (176) 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 ---------------------------------------- (177) 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 ---------------------------------------- (178) 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 ---------------------------------------- (179) NarrowingProof (BOTH BOUNDS(ID, ID)) Narrowed the inner basic terms of all right-hand sides by a single narrowing step. ---------------------------------------- (180) 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 ---------------------------------------- (181) 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 ---------------------------------------- (182) 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 ---------------------------------------- (183) 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 ---------------------------------------- (184) 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 ---------------------------------------- (185) SimplificationProof (BOTH BOUNDS(ID, ID)) Simplified the RNTS by moving equalities from the constraints into the right-hand sides. ---------------------------------------- (186) 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 ---------------------------------------- (187) 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 ---------------------------------------- (188) 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 ---------------------------------------- (189) 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 ---------------------------------------- (190) 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.